Question

Resolver

x2 + y2 = 20;

xy = 8

x> 0; y > 0; x > y

Indique como respuesta un valor de x-y

Answer 1

$y=\dfrac{8}{x}\\ \\ x^2+\dfrac{64}{x^2}=20\\ \\ x^4-20x^2+64=0\\ \\ (x^2-16)(x^2-4)=0\\ \\ \boxed{x\in\{2,4\}}\\ \\ \boxed{(x,y)=(4,2)}\\ \\ \\ \boxed{\boxed{x-y=2}}$