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Пікірлер: 203
@richardatkinson47102 ай бұрын
That algebraic method isn’t a method at all. You can’t set off on a series of substitutions in the hope that you might end up with an easily recognizable perfect square. The “problem” has been constructed from the “solution”.
@YAWTon2 ай бұрын
I disagree. Once that it is recognized that 64^2+49^2+15^4 has the form x^4+y^4+(x+y)^4 the result follows from straightforward algebraic transformations. No guessing involved. Of course, in the absence of this insight, it is also not difficult to use basic arithmetic to obtain the result 169.
@richardatkinson47102 ай бұрын
@@YAWTon You are right, but my point is that the “method” outlined does not mention that insight. The double substitution is totally unnecessary. (Do you agree?) You either notice that you can factorise, in which case you should (and you did - as did I when I saw this) or you go through the arithmetic.
@richardatkinson47102 ай бұрын
@@YAWTon It’s over 50 years since I did any maths, but the substitutions vaguely recalled the solution to the general quartic. Is that how the “problem” was conceived, do you think?
@YAWTon2 ай бұрын
@@richardatkinson4710 I agree that his presentation was bad for the reasons that tou mentioned. Too many intermediary steps. Apparently the problem suggests a "solution" that is invalid, but leads to the correct value (based on the assumption that the squareroot of a sum equals the sum of the squareroots of the terms of the sum).
@LuluLaSaumure2 ай бұрын
It is a math olympiad problem ! Of course, the problem has been built from the solution : it is meant to be solved this way. This is how the math olympiad jury makes to find the best students : by their abylity to find the right substitution at the right moment of the calculus and their ability to lead such a huge calculus until its end ! In real life maths, you hardly find such calculus but in a maths competition it's classic that people have to use such tricks
@Baltie32 ай бұрын
I guess calculating it directly would take less time.
@oboumami61862 ай бұрын
You are absolutely right, it is around eight times faster.
@eduardofs6620Ай бұрын
Agree. It seems that many people doesn't knows the basics, or how make some basic arithmetic operations (using elementary knowledge, and a pencil and a sheet of paper if necessary)
@Baltie3Ай бұрын
@@eduardofs6620 and inclusive philosophy requires everyone to prove slowly, in small steps, that 1+1=2 😀
@rexwu5042 ай бұрын
This is Candido's identity in disguise, [x^2 + y^2 + (x+y)^2]^2 = 2[x^4 + y^4 + (x+y)^4]. Candido used the Fibonacci numbers in his original publication.
@runninggreenhorn91852 ай бұрын
Haven't been doing this for more than thirty years ... and never missed it. 🙂
@joansola023 ай бұрын
The fourth root would have allowed for an extra simplification, giving 13 as the final result 😊
@udayabose23572 ай бұрын
Why not just long multiply, add, divide by 2 and then find the square root? Much simpler.
@vpgmiramar2 ай бұрын
Nice. Elegant.
@villiamo38613 ай бұрын
Excellent. Thank you.
@schlingel00173 ай бұрын
There is no need to open the paranthesis of 4th power. You could do the second substition before that.
@ashokpandey58282 ай бұрын
Nice
@learncommunolizer2 ай бұрын
Thank you very much!
@artyonehundred3 ай бұрын
169 is 13^2, so is there further simplification to be done at the 8^2 + 7^2 + 8 x 7 stage?
@kevinsnell16222 ай бұрын
I think the power of math practice is working these out long hand, verbally calling out as you go, with pencil on paper. You develop so many other skills through this process. Agreed time consuming but worth the time especially if you are a slower learner.
@user-fb1qo8go1b3 ай бұрын
Прекрасная задача и великолепное объяснение ее решения. Мне 72 года и моя профессия не связана с математикой, но мне все понятно и интересно. СПАСИБО
@indigopeach3 ай бұрын
Ow! My brain!
@glotelu2 ай бұрын
Siento que la pudo resolver fácilmente desde un inicio sin tanto rollo.
@lukaszek77722 күн бұрын
Don't need to make any x or ys, after the first = you have (8+7)^4, that is 8^4+7^4+2x56^4. So now you easily divide all by 2, end up with 8^4+7^4+56^2 all under square root, do the root, done
@pingupenguin2474Ай бұрын
I could do this, if necessary, as I was taught long multiplication in primary school !
@bladimirjgt2 ай бұрын
Vamos a resolver el problema paso a paso.Primero, definimos la operación:[ \sqrt{\frac{64^2 + 49^2 + 15^4}{2}} ]Calculamos cada potencia:[ 64^2 = 64 \times 64 = 4096 ][ 49^2 = 49 \times 49 = 2401 ][ 15^4 = 15 \times 15 \times 15 \times 15 = (15^2)^2 = 225^2 = 50625 ]Sumamos los resultados obtenidos:[ 4096 + 2401 + 50625 = 57122 ]Dividimos la suma por 2:[ \frac{57122}{2} = 28561 ]Calculamos la raíz cuadrada del resultado:[ \sqrt{28561} = 169 ]Entonces, la respuesta es:[ \boxed{169} ]
@Blisssource2 ай бұрын
Is this a solution or substantiation?
@terencetwentyman-jones88612 ай бұрын
That would give me writers cramp.....and why would I ever need to do it....
@irinabaigozina85513 ай бұрын
Супер мега задача! Thank you so much for it! It's perfectly cool
@learncommunolizer3 ай бұрын
Thank you very much!
@unbeaunom3 ай бұрын
Cool. I loved it.
@sthi33962 ай бұрын
A nice radical math complication.
@teej1432 ай бұрын
The solution made the problem seem more complicated. I don’t need a calculator nor do I need to use this method to find the same exact answer.
@glennmann6343 ай бұрын
Brilliant!
@FedorLyudogovskiy2 ай бұрын
169 = 13^2 = 8^3 - 7^3
@RacvaddАй бұрын
I'm pretty bad with math and i can't do all this process. If the goal is solving this operation without using calculator, based on my math memories, wouldn't it be easier just rewrite as: 64+49+15^2/2?
@yasnac75762 ай бұрын
Step seven you forgot the clouser ')' but it doesn't affect the final answer.thanks for the solution....😊
@saadalikhan92102 ай бұрын
Should've used a^2 + b^2 + c^2 form
@PatrickCazaux3 ай бұрын
Was the first substitution necessary ?
@bvenable783 ай бұрын
No substitutions are _necessary_; they just make the algebra easier. I like that he did the two substitutions; it breaks the problem down into smaller steps, making it more accessible to viewers - especially those that aren't practiced enough at algebra to follow skipped steps.
@okiedoak20127 күн бұрын
So...all this is nice and dandy...show this example by going to the grocery store and getting dinnner....
@cyprianalford36192 ай бұрын
OMG
@paperthinpizzaАй бұрын
169. Took me 20 seconds on my calculator. Simple arithmetic following the order of operations. No need for fancy math on this one
@tiramisu002 ай бұрын
±169
@MathSync3 ай бұрын
i ❤ Mathematics
@michelvondenhoff967321 күн бұрын
Depends on where you live.
@gaskellr442 ай бұрын
Good old Pascal
@anatolykatyshev93883 ай бұрын
I have much better solution. Everybody knows that 64^2=4096. 49^2=2401 15^4=225^2=50625 Half sum of it is 28561, which is square of 169, also known fact.
@Swannerator3 ай бұрын
"Everybody knows that..." - tell us that you cheated and used a calculator without telling us that you cheated and used a calculator. 🤡
@anatolykatyshev93883 ай бұрын
@@Swannerator Author also used calculator to find square roots of 64 and 49. It is not easier , than 64^2 and 49^2!
@olegkobyzev18843 ай бұрын
@@Swannerator no need in calculator, that numbers are small (easy to multiply in mind), and even if you not remember 169^2 you can just calculate it on paper.. every one knows
@maas_ter3 ай бұрын
@@anatolykatyshev9388everyone knows sqrt of 64 and 49 💀
@gagwong89642 ай бұрын
Concur, way much better than fiddling all that ↑↓←→abxy口O∆ around 🤦🏻♂️
@evilnewbie1129 күн бұрын
Now I know why we invented the calculator…
@oliverdauphin2362 ай бұрын
Très astucieux. Bravo !
@learncommunolizer2 ай бұрын
Thank you very much!
@JoseManuelSosaGarcia3 ай бұрын
169
@himadrikhanra74633 ай бұрын
15× rootover 226..?
@user-pi2my7vk5j2 ай бұрын
Математика как Поэзия! Им ночью снятся Арктики и Звездные Галактики, ведь математик- это Фантазёр!
@dhanasekaransundaram41413 ай бұрын
Very nice
@learncommunolizer3 ай бұрын
So nice, Thank you very much!!!
@tlgergun7470Ай бұрын
15×15
@gaskellr442 ай бұрын
Ans = 169 or even 13^2
@asyaasya21442 ай бұрын
Математика это жизнь!!!
@aadil_1998Ай бұрын
Square root can be written as into the power (1/2).... = [((64^2)+(49^2)+(15^4))^1/2]÷2 Multiply the power with every number inside... = [(64^2)^1/2 + (49^2)^1/2 + (15^4)^1/2]÷2 = (64+49+15^2)÷2 = (64+49+225)÷2 = 338/2 = 169 Done
@MT_Hearts4 күн бұрын
You forgot about √2 as the denominator.
@VincentLauria62 ай бұрын
Surprised he didn’t end it with 169 = 13^2
@richardatkinson47102 ай бұрын
Or start with root root…
@tamarshahverdyan27232 ай бұрын
140
@cantemirash2 ай бұрын
Nice writing skills.😂
@AlenaSlavic3 ай бұрын
Легче все перемножить , будет корень из 28561=169.
@handchess2 ай бұрын
13²
@dwshow15Ай бұрын
√64^2+49^2+15^4/2 ok Then, you can kick to root 😁, then outstanding is 64+49+15^2/2, 64+49+225/2, 338/2 = 169 ✔️ simple 😂😂😂😂😂
@stuartcockroft43652 ай бұрын
328
@Shirokuma153 ай бұрын
No, this is too long..sometimes question like this in a test only give you 1 to 2 minutes to solve,.
@fernandopobletebyfepo48203 ай бұрын
Prefiero seguir programando en asembler
@babsiw71642 ай бұрын
Wer brauch sowas
@vicenteayllonperez28793 ай бұрын
Y no le veo ningún aporte a las matemáticas
@guptajii74953 ай бұрын
120√2 solution 😢
@gagwong89642 ай бұрын
Are we not doing √ as the last step to get ±169 as answer?🤔
@mickaelbazola8492 ай бұрын
No, a square of number is positive
@go_gazelle2 ай бұрын
In algebra, the radical sign typically indicates the positive root only. A ± sign in front would indicate both roots. (y = sqrt(x) has no negative values for y.) However, I wouldn't say it's wrong if you include -169 as a second answer. I actually like that since the problem presents as arithmetic.
@gagwong89642 ай бұрын
Thank you both for clearing my doubt.🙏🏻 I indeed went back to read about the basics . It says something like this : square root of a number is always positive, only in functions or equations like y=x², x has two values, the positive and the negative.
@go_gazelle2 ай бұрын
@@gagwong8964 I think that's basically correct. But y = x² seems like a strange example. A better example would be 9 = x². Here x = ±3. Or a = x². Here x = ±sqrt(a). Whereas, y=x² should be interpreted as a function in which there are infinite values for x.
@richardatkinson47102 ай бұрын
@@go_gazelle Quadratic equations have two roots.
@user-lw1ct2zc9fАй бұрын
169. 5 minutes in mind.
@matsonnerby2 ай бұрын
So much simpler than using a calculator 😂
@sirajuddinshaikh188323 күн бұрын
I know
@golavlАй бұрын
Икату жжот. Зачот )
@phil4499Ай бұрын
Lost me at 2.40 😮
@richardshaw66642 ай бұрын
Moral: when learning math, don't use KZfaq. 😂
@eduardofs6620Ай бұрын
Can we complicate things? Let's do it! Or... how to make things worse than they really are...
@Physics4every12 ай бұрын
SO SIMPLE. DO THIS AND DO IT IN YOUR HEAD. If you know the rules. Solved it my head in seconds. Here's how. The square root is basically x^1/2 so using distribution that kills 2 from each exponent leaving [(64+49+225)/2] = (338/2)= 162. Easy
@LarghettoCantabile2 ай бұрын
An interesting coincidence insofar as generally the square root does not distribute over terms. The numbers were probably chosen precisely because this coincidence is a trap.
@ArturJarosik2 ай бұрын
I've done it exactly the same.
@philmach65857 күн бұрын
338÷2 are 169 btw
@russomarioaa3 ай бұрын
Giochi di teoria , con calcolatrice vai subito alla soluzione😊 comunque ottima conoscenza👍
@hongthanhtran99443 ай бұрын
Thanks! Step 6 you lose )
@sharjeelshafqat652829 күн бұрын
Difficult and lengthy
@juliushafsteinsson767514 күн бұрын
Fram ÍA
@kentbrooks32273 ай бұрын
This is why I changed my major to music!
@loganshaw45272 ай бұрын
College mathematics is just different. I loved exponentials as a kid did not learn of the different elevations until later. I know equal and above but not not learn much of below. But only learned to the end of highschool.
@Lemda_gtrАй бұрын
Calculator answer is 57.97 🧐
@ilevitatecs2Ай бұрын
Good lord this is not even close to being an efficient solution.
@user-sr6uy2oy4xАй бұрын
WHY NOT ASK CHATGPT TO USE DIRECT COMPUTATION AND ALGEBRAIC METHOD. NONE AS DIFFICULT AS ABOVE METHOD.
@dannyroosenboom36403 ай бұрын
sqr30705
@dwshow15Ай бұрын
169 can come in just 10-15sec. 😂😂😂😂😂😂😂😂
@Kooliat3 ай бұрын
Haaaaa bic mac
@ShoaibKhanZ2 ай бұрын
The only mistake was canceling the root with the square. Should have been written with +/- (a+b).
@davegilmour1895Ай бұрын
Use a calculator/phone
@sylvesterogbolu-otutu1498Ай бұрын
If you took the square root and simplified the values under the radical sign, you will get: (sqrt(64)^2) = 64 (sqrt(49)^2) = 49 (sqrt(15)^4) = 15^2 = 225 64 + 49 + 225 338 ---------------------- = ------- = 169 2 2 The answer is 169
@dwshow15Ай бұрын
😂😂😂😂😂😂
@UniqueNewYork273 ай бұрын
Guys, I just took the sqrt and squared exponents and cancel them out, then it'll be 64+49+(15)^2/2 Secondly, 64+49+225/2 Lastly, 338/2 Now you have your answer of 169, i didn't even learn this at school yet💀
@phoebe5433 ай бұрын
The denominator wasn’t squared
@Swannerator3 ай бұрын
I hope you pay attention in Maths class when your class gets up to this. 🤦🏻♂️
@UniqueNewYork273 ай бұрын
I didn't even learn this at school yet lol
@popolaminc61883 ай бұрын
🤦♂️Unexplainble, but you got the right answer
@irenebeltranruiz34312 ай бұрын
I did the same!
@CyBeatsSs3 ай бұрын
Too much steps
@bvenable783 ай бұрын
I expect he did that for instructional purposes, and to make the solution accessible to viewers with less practice in algebra.
@Crusader-George2 ай бұрын
not really, it's doable compared to sqrt thousands lol
@irenebeltranruiz34313 ай бұрын
Another solution First we know that √ is the opposite of ^ So √ 64^2 = 64 So √49^2 = 49 So √15^4 = 15^2 Because 4 - 2 = 2 So we have 64 + 49 + 15^2 And you know that 15^2 = 225 So 64 + 49 + 225 = 338 338 / 2 = 169 Can you do without pencil and paper?
@rcyu2 ай бұрын
Don't you have to distribute the square root to 2 as well?
@gagwong89642 ай бұрын
√(a²+b²+c²) ≠ a+b+c
@marcherrmann96352 ай бұрын
Pure coincidence?
@keescanalfp51432 ай бұрын
@@gagwong8964, in spite of all we see that it still works, at least for her.
@mikemercury3656Ай бұрын
Can you go a little slower!
@GEILTOYАй бұрын
You did too complicated. There is easy way without Calculator
@feroxnando2 ай бұрын
Too much paper its not simplifing
@gandhimahatma33043 ай бұрын
I’m not advanced by any means but so many unnecessary steps. Neat little arithmetic problem though
@user-hq3uj4hx1w2 ай бұрын
just calculated in my head and got the result of 169 without draw more than a full papersheet the root of 64 and 49 squared is just 64 and 49 plus 15 squared ist 225 338 half is 169 it was less than 1 minute
@Physics4every12 ай бұрын
Same here wrote my comment then came to see how other people are screwing this up.
@comdo7773 ай бұрын
asnwer=9 os isit
@gato_catindig2 ай бұрын
i just removed the squares and made 15^2/2 i got the same answer lol
@grafeebabee2 ай бұрын
why not first get rid of the square root bracket by reducing the numbers to 64 +49+15^2...add those then divide by 2 and you still get 169 and the square root of that is 13....
@alexgrebenschikov46383 ай бұрын
Toooooo long solution
@SaiteZwei2 ай бұрын
I'm sorry, but this is absolutely dubious click bait bullshit. The video has nothing to do with a serious mathematical solution algorithm. the solution only works for exactly these numbers. The task was developed backwards from the solution and is in no way transferable to another example.
@andyohil74652 ай бұрын
Are you crazy? The solution is quite simple and take never a minute to solve: (64 + 49 + 225) / 2 = 169
@MT_Hearts4 күн бұрын
Denominator will be √2. Cannot ignore that.
@RobbieIsbell3 ай бұрын
WFT? I DID IT IN 3 STEPS. 169
@marcherrmann96352 ай бұрын
Elaborate further, please....
@RobbieIsbell2 ай бұрын
@@marcherrmann9635 Seriously? It's easy: First we know that √ is the opposite of ^ So √ 64^2 = 64 So √49^2 = 49 So √15^4 = 15^2 Because 4 - 2 = 2 So we have 64 + 49 + 15^2 And you know that 15^2 = 225 So 64 + 49 + 225 = 338 338 / 2 = 169
@TonyQl2 ай бұрын
@@RobbieIsbell you can’t do that because root of a + b is not equal to root a + root b
@brunobastos55332 ай бұрын
I never understand why they add so many steps . Like all numbers are 2 or power of 2. They do it like pc's not stray from the way they learned it even if the solution is infront of them