Olympiad Math Equation. Try it first!! Improve your Math.

[@saityusufbulur3366]

Thanks for the video, here's another solution:
x + y = 5/2
x^2 + y^2 = 13/4
(x + y)^2 = x^2 + y^2 + 2xy = 25/4
13/4 + 2xy = 25/4
2xy = 12/4 = 3
xy = 3/2
x = 3/2y
x + y = 5/2
3/2y + y = 5/2
3/2y + 2y^2/2y = 5y/2y
3 + 2y^2 = 5y
2y^2 - 5y + 3 = 0
(2y - 3)(y - 1) = 0
y = 3/2 and x = 1
or
y = 1 and x = 3/2
Either way, answer = 1^5 + (3/2)^5
1^5 = 1
(3/2)^5 = 3^5/2^5 = 243/32
1 + 243/32 = 275/32 ✅