Question

If x^2 + y^2 = 10 and xy = -3, what is the value

of (x - y)^2?

A) 12
B) 16
C) 20
D) 25

Answer 1

Explanation:

`xy=-3,\ x=-(3)/(y)\\ \\ x^2+y^2=10\\ \\ (9)/(x^2)+x^2=10\\ \\ x^4+9=10x^2\\ \\ x^4-10x^2+9=0\\ \\ (x^2-1)(x^2-9)=0\\ \\ (x-1)(x+1)(x-3)(x+3)=0\\ \\ x=-3,-1,1,-3\ y=1,3,-3,-1\\ \\ (x-y)^2\\ \\ (-3-1)^2=(-4)^2=16`