Italy | A Nice Algebra Problem | Math Olympiad

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Find the value of x and y?
How to solve x^y - y^x = 17
In this video, we'll show you How to Solve Math Olympiad Question A Nice Exponential Equation x^y - y^x = 17 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #maths #math #algebra

[@ahmedbourht1820]

1^-16-(-16)^1=1/1^16-(-16)=1/1+16=1+16=17 so s=((3,4), (18,1),(1,-16))

[@SALogics]

Very nice! ❤

[@dardoburgos3179]

X= 18, Y= 1. Tiene infinitas soluciones. Eso y mucho ➕ lo aprendí en la escuela pública.

[@sy8146]

Thank you for explaining. There are other solutions. They are (x, y)=(18, 1) and (x, y)=(1, -16) . I wrote with miss-typing, so I changed to correct sentences.

[@SALogics]

Very nice! ❤

[@SGuerra]

A questão é bonita, mas é necessário especificar que x e y são números naturais, de acordo com a solução apresentada. Na verdade há mais de uma solução para essa questão. Brasil Outubro de 2024.

[@SALogics]

bela sugestão! Eu realmente aprecio isso ❤

[@LITHICKROSHANMS-gw2lx]

My solutions x=18,y=1 x=3,y=4

[@SALogics]

Very nice! ❤

[@nasrullahhusnan2289]

(x^y)-(y^x)=17 Trivial solution: (x^y)-(y^x)=18¹-1¹⁸ (x,y)=(18,1) Another solution: 17=(x^y)-(y^x) =[(x^(½y)]²-[(y^(½x)] =[{x^(½y)}+{y^(½x}][{x^(½y)}-{y^(½x}] [x^(½y)]+[y^(½x}]=17 [x^(½y)]-[y^(½x)]=1 Summing: 2x^(½y)=18 x^(½y)=9 x^y=81 --> (x,y)={(9,2),(3,4)} Differencing: 2y^(½x)=16 y^(½x)=8 --> y^x=64 =4³ (x,y)=(3,4) Therefore (x,y)=(3,4)

[@SALogics]

Very nice! ❤

[@MananArhamOP]

Why are these equations named after countries??

[@SALogics]

Because these questions are from international exam cometitions math olympiad ❤

[@rafaelfelipe4753]

Trivial. x=3 e y=4

[@SALogics]

You are right! ❤

[@alphazero339]

Trivial and you still got it wrong