Oxford University School of Pure Mathematics Admission Interview

[@raghvendrasingh1289]

Let x+y = t then x-y = 64/t Now (x+y)^2- (x-y)^2 = 4 xy hence t^2- 4096/t^2 = 32 t^4 - 32 t^2 = 4096 making perfect square (t^2-16)^2 = 4096+256 (t^2-16)^2 = 256(16+1) t^2-16 = 16√17 (rejecting negative sign ) t^2 = 16(1+√17) t = √{16(1+√17)} , - √{16(1+√17)}

[@RyanLewis-Johnson-wq6xs]

X^2-Y^2=64 XY=8 X+Y=±4Sqrt[1+Sqrt[17]]

[@9허공]

let a = x + y, b = x - y => x^2 - y^2 = (x + y)(x - y) = ab = 64 xy = ((x + y)^2 - (x - y)^2)/4 = 8 => a^2 - b^2 = 32 => a^2 - (64/a)^2 = 32 => a^4 - 32a^2 - 64^2 = 0 => a^2 = 16(1 + √17) => a = x + y = ±4√(1 + √17)