s=3 9³-3³= 729-27 702

Please stop calling trivial problems "Math Olympiad"!

By squaring u get aSuare plus b square plus 2ab. You know the value of ab as 6. By squaring RHS becomes 36. 36- 2abwhich is 12. So you get a square plus b square as 24. In this either for a or for b substitute either a=6/b or b=6/a. Then you get a quadratic equation either in a or in b as the case may be. You get two values for b. Similarly u get two values for a. Hence the answer

How do you decide that 27 +3 thing. Why not 20 and 10 29 and 1 etc. That step is never explained.

По какому основанию логарифм?

33^(44/33) > 44. By a lot.

NOT an Olympiad problem!! Trivial 101 algebra.

Unfortunately, the solution provided by the author of this video is incorrect. He/she has made a mistake that is commonly seen on KZfaq math videos. It arises from a misinterpretation of the exponential notation of the problem. It is universally understood and accepted that the notation A^y, where A is a constant or function, indicates that the function or constant A is to be raised to the power y. In this case, the function A is x^x and the power y to which A = x^x is to be raised is 5. The result of raising A = x^x to the fifth power is to equal 100. Using parentheses to make definite the required sequence of operations in accordance with the aforementioned meaning of an exponent, the expression to be solved for x is (x^x)^5 = 100. To solve for x, first take the fifth root of both sides of the equation. The result is (x^x)^5/5 = 100^1/5 or x^x = 100^0.2 = 2.511886432. Next, take the natural logarithm of both sides of x^x = 2.511886432, that is, x ln(x) = ln(2.511886432) = 0.921034037. [Any logarithm base will do, but the intermediate numerical values in the computation will differ]. The value of x that solves x ln(x) = 0.921034037 is x = 1.712361705. The claimed result, 10^1/5 = 10^0.2 = 1.584893192, is incorrect. One can readily verify that (1.712361705^1.712361705)^5 = 100.

At first I thought you were going to do a solution that doesn't involve logarithms, but then you used log at the end anyway. In that case, you can just calculate log48/log4

How is 3rd step Solved...?

2 seconds !

🤯😍

Any programmer would immediately write 32768 + 4096 + 512 + 64 + 8 and add them up.

He just keeps repeating the same stuff - totally clueless

I think Super best tutor Ever...❤ Keep it up Sir... What is the need of 1k Subs...

Sir How the property of logarithum you used.....?

Waoooo....Two Methods.....❤😊

You Solved it Interestingly but i Solved it in Seconds.....❤

a= 3

That could have been solved in 3 steps tops.

This is why kids struggle with math. This was the most amazingly complicated and opaque solution possible.

root 12 = 2 root 3

There are 2 more solutions: m=1.7649219... and m=-0.778373...

At the start itself this could have been multipled and divided by √108+√81

5^7/8=5^3x so 3x=7/8 and x=7/24 my god 8:34 minutes for this that's very ugly math, you can do this by heart

Excellent

a=3 Это видно из разложения на простые множители числа 702.

Thanks too much, your illustration is optimum acceptable and simple state, thanks again

would it not just be way way easier to say that 5 = (125)^(1/3). Then substitute 5 for 125^1/3 in the original equation and write the square roots as a power of 1/2. Then just use standard calculation rules to get the correct power.

We can take integers from 0 to beyond in the negative spectrum, and boom i got -3

这口算能力看着就着急，中国学生可以少写很多步骤，起码少一半时间做完

No imaginary solutions?

Can't you do this much more quickly, ie cube root everything giving 2x +8=2. Then it's easy?

Really bad solution. Proper one: divide numerator and denominator by sqrt(3) to obtain (1-2)/(1+2)=-1/3. Math Sync - learn math before teaching one.

tried this in my head, I got (-6 +/- 6I√(3) )/-2, which is at least similar to the answer they got 😅

You evercomplicated it for no reason. You just multiply the powers and you get immediately 8^4*8^2*8 = 8^7

How to invent or imagine something that only exist if you "believe in it" [yes I was taught something like that in school ( in the 1960-ties) but didn´t see why it was necessary to invent something that only existed in the mind of my teacher (at that time)] well, well things happen!

I don't understand why all the trouble. 6^x=12 => x=log6(12).

basic 10th grade high school math

Since both have to be positive, considering both the sum and the product are positive, if we're looking at real value'd solution we get a = 6-b => b(6-b) = 6b - b^2 which is strictly smaller than 36 for a,b <= 6 and therefore no real solutions exist and we have to look at complex solutions. Since the sum is real and not complex, the imaginary parts has to be equal but opposite, i.e we're looking for a conjugate pair where the real part is 6/2 = 3. So we have a = 3 + yi; b = 3 - yi ab = 9 + y^2 y^2 = 36 - 9 = 27 a = 3 + sqrt(27)*i; b = 3 - sqrt(27)*i And of course the second solution is simply switching the values of a and b around. So much unnecessary work in this video.

It may be easier if you use the following approach: a + b = 6 ----> [1] a b = 36 ----> [2] (a - b)^2 = (a + b)^2 - 4 ab (a - b)^2 = 6^2 - 4 * 36 Froma [1] and [2] (a - b)^2 = 36 ( 1-4) (a - b) = +/- 6 √(-3) a - b = +/- 6 i √3 ----> [3] 2a = 6 +/- 6 i √3 From [1]+[3] a = 3 +/- 3 i √3 2b = 6 -/+ 6 i √3 From [1]-[3] b = 3 -/+ 3 i √3 (a, b) = { (3 +3 i √3, 3 - 3 i √3) , (3 -3 i √3, 3 + 3 i √3) }

You made a mistake @2:17 you should have written (x-7)[(x²+7x+49)+1] instead of (x-7)[(x²+7x+49)]+1. In the next step you made a second mistake that corrected the first one so no harm is done in the end.

Tried solving it in my head, then realised the solution must be a complex number. So I gave up calculating it in my head.

If that wasn't a complete waste of time and effort, what was it? And what does the weird upside down "?" mean? 😵‍💫

The third part of step 2 should be negative b squared plus 6b minus 36 shouldn't it?

8^7

NICE One....❤

I was solving this problem during 10 seconds: a = -7, b = 6

Ais -7 and Bis +6.

My second chennal Please show support by like and subscribe: youtube.com/@8minutesexplainer?si=tsZkdtz1kcJgETVn