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Пікірлер: 43
@johnmccullagh27054 ай бұрын
Good solid algebra. Yes a bit slow, but for someone like myself who has not done much serious math since student days (half a century ago now), better to include all the steps rather than skip some. And yes, the obvious real solutions from simple inspection are x=2, y=1 and x=1, y=2, however that's not the point of the exercise. Whether it's a good Math Olympiad problem or not, I'm afraid I can't judge.
@TWJRPGGamming7 ай бұрын
x=2.y=1 x=1,y=2
@neel333neel3 ай бұрын
thanks
@learncommunolizer3 ай бұрын
You're welcome!
@KipIngram4 ай бұрын
By "looking at it and thinking for a second," x=2, y=1 and x=1, y=2 are solutions.
@catiaman2086 ай бұрын
this has sipleset way since the numbers of X AND Ymyst be integer X+Y=3 RESULT X=1 and Y=2 X5+y5=1+2^5=1+32=33
@ryanchiang95876 ай бұрын
x = 2, y = 1 or vice cersa
@user-nd7th3hy4l2 ай бұрын
(1;2) (2;1)
@rafielmesaias5 ай бұрын
We have an equation of grade 5. But you have just four roots or solutions por x and y
@GFlCh4 ай бұрын
While it might be nice to see how to work out another solution, it's possible any additional solution would be extraneous, or a duplicate of an existing solution. But most importantly, any valid solution for the problem as a whole, has to work in both equations, and another solution to the "x⁵ + y⁵=33" equation, if it exists, might not work in the "x + y = 3" equation.
@user-dq3uh6ee5w3 ай бұрын
Such system has 5 solutions or less.
@sudarshandutta24982 ай бұрын
X= 2/1, Y=2/1.
@user-dq3uh6ee5w3 ай бұрын
(1, 2), (2, 1). They €R².
@prayitsmg70866 ай бұрын
X = 1 , Y = 2 or X = 2 , Y = 1
@arturmadatyan48926 ай бұрын
Очень простое уровнение, почему так мучается?
@user-ye6go4ft7q5 ай бұрын
Надо немножко подумать,потом мучатся,точно !!!
@heniwatisetiono69957 ай бұрын
x=1, y=2 or x=2, y=1
@ArashHormozi-xx3mu6 ай бұрын
X:2 y:1 or x:1 y:2
@guyhoghton3997 ай бұрын
You can use the identity _uₘ₊ₙ = uₘuₙ - uₘ₋ₙ(xy)ⁿ_ where _uₙ = xⁿ + yⁿ_ Thus: _u₀ = 2, u₁ = 3, u₅ = 33_ _u₂ = u₁² - u₀(xy)¹ = 9 - 2xy_ _u₃ = u₂u₁ - u₁(xy)¹ = 3(9 - 2xy) - 3xy = 27 - 9xy_ _u₅ = 33 = u₃u₂ - u₁(xy)² = (9 - 2xy)(27 - 9xy) - 3(xy)²_ ∴ _243 - 135xy + 15(xy)² = 33_ ⇒ _(xy)² - 9xy + 14 = 0_ ⇒ _(xy - 2)(xy - 7) = 0_ ∴ _xy = 2_ or _7_ Note that _x_ and _y_ are the roots of _t² - (x + y)t + xy = 0_ Case (i): _xy = 2_ _t² - 3t + 2 = 0_ ⇒ _(t - 1)(t - 2) = 0_ ∴ _x, y = 1, 2_ in either order. Case (ii): _xy = 7_ _t² - 3t + 7 = 0_ ⇒ _t = ½[3 ± √(9 - 28)]_ ∴ _x, y = ½(3 + √19), ½(3 - √19)_ in either order.
@Verdiw7 ай бұрын
I graph it in demos , only 2 real sol Edit : Sadly at the last part you messed up 9-28 is -19 not 19 so 2 complex roots
@wongkienloon5 ай бұрын
33+3+33+3=72 66+6=72 (66/72) + (6/72)=1=100%
@user-nd7th3hy4l7 ай бұрын
X=2 et Y=1
@neilmccafferty58867 ай бұрын
you can see it must be 2 and 1 immediately.
@user-lf1bm8fm2g7 ай бұрын
Комплексные корни не интересны.
@neilmccafferty58867 ай бұрын
@@user-lf1bm8fm2g has to be integers, both greater than 1. simple.
@Verdiw7 ай бұрын
@@neilmccafferty5886Doesn’t need to be integer
@user-cp5wu5pg1o3 ай бұрын
Это же устно решается, сразу в глаза бросается, что х=1, у=2 или х=2, у=1.
@user-dq3uh6ee5w3 ай бұрын
Hо система может иметь др. решения.
@is77287 ай бұрын
Can anyone explain why there are only 4 roots, not 5?
@Verdiw7 ай бұрын
An degree n equation doesn’t need to have n distinct root , some can be the same so the amount of root is not more than n
@is77287 ай бұрын
@@Verdiw I know that so which one is the double root?🌲
@nemesiochupaca50246 ай бұрын
Porque si sustituyes y=3-x Te va a quedar x^5+(3-x)^5-33=0 y el término quíntico se irá, quedando un polinomio de grado 4
@markterribile69486 ай бұрын
Who is your audience? Your audience is people who can appreciate and learn what you are showing them. Such people must have mastered high school algebra, and have presumably mastered grade school arithmetic, preparing them to learn the more advanced techniques and principles you are showing them. They--we--don't need to see basic numerical division belabored. They--we--don't need the detailed steps of factoring a quadratic. With the factors given, we need about three seconds to verify them, then we can move on. The value in these solutions is the overall scheme, recognizing the larger patterns that we can use to pry the problem apart. But you bury those steps in the minutia that we have already mastered, making it hard to find the precious grains of gold mixed with the dross of first year algebra and fourth grade arithmetic. These are brilliant solutions. The presentations would be so much better if you demonstrated the brilliance and moved routinely through the routine mechanics.
@calcnoon6 ай бұрын
・・これを日本の大学入試は 5分以内で全てやらにゃあかん。 このスピードでは既に不合格。
@user-wu6jj5no7k5 ай бұрын
Supposed to be 5 roots
@CrYou5754 ай бұрын
If you set x = 3-y using equation 2 then the highest term of x^5 is - y^5, which cancels out with y^5 in equation 1. This reduces the problem to solving a quartic and results in four roots.
@user-dq3uh6ee5w3 ай бұрын
5 or less.
@supermanusa48285 ай бұрын
X^5 + Y^5 # (X + Y)^5
@user-jp2ow1cj1l7 ай бұрын
Х=1, У=2 ; У=2, Х=1.🙉🙉🙉🙉🙉
@williammarshal40436 ай бұрын
Evaluate before doing all of your shit. If x+y = integers. and x⁵+y⁵= integer then x and y is integer then evaluate b²-4ac, if it's negative, stop. No point of continuing, i^odd integers. Will always has I as result.
@edwardwang79297 ай бұрын
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@MarcelCox16 ай бұрын
Sorry, but I find your video disappointing for 3 reasons: 1. You did not specify in which domain you are solving, integers? real numbers? complex numbers?. You solved for complex, but you did not specify in advance. In math alympiads, problems are always specified more precisely. You omitted important information. This is an error often commited by a number of people doing this kind of videos, and I find it hugly annoying. 2. Your solution is correct but the problem can be solved more easily. In this kind of problems, there are often more efficient approaches than the brute force method. The colculations get easier when you realise that that x5+x5=(x+y)(x4-x3y+x2y2-xy3+y4) and continue from that. You then only need 4th and second powers of (x+y) which makes the fomulas a little bit simpler and thus less error prone. 3. This comment is mino: state your sources. Like xxx math olympiad problem from yyyy where xxx is the orangisation/country or whatever and dddd is the year. For poitn 3, I have the impression that many youtubers just copy the problems from other youtube videos as while there are so many interessing math olympiad problems, you oftend find the same problems over and over again.