Nice Math Olympiad Algebra Problem | How to solve? | (X,Y) = ?

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• Japanese | Can you sol...

[@Rohmat-oo3pw]

X²-y2-y+x=0. X²-y ²+x²-y=0. (X+y)(X-y)+(X-y)=0. (X+y)+1=0. -y=x+1. X²-y=73. X²+x+1=73. X²+x-72=0. X²+9x-8x-72=0 (x+9)(x-8)=0 x=-9 and x=8. X+y+1=0. Y=8 and y=-9 X

[@madurappankalyanaraman8015]

x,= 8 y= -9
8²-(-9) =64+9=73
(-9)² -8 ,81-8=73

[@HeikoBoekstiegel]

There are two more solutions (x,y), because you do not consider the case x = y. (2:21) Hence solve also x² - x = 73.

[@CharlesChen-el4ot]

x^2-x=y2-y
(x-y)*(x+y-1)=0
x=y or x+y = 1
x^2 - x =73
x = 1/2(1+/- (1+292)^1/2