If $x + y = 8$ and $xy = 15$, find $x^{2} - y^{2}$ given $x y$.

Question

If $x + y = 8$ and $xy = 15$, find $x^{2} - y^{2}$ given $x > y$.

Aicharya · Accepted Answer

$(x-y)^{2} = (x+y)^{2} - 4xy = 64 - 60 = 4 \Rightarrow x - y = 2$. Then $x^{2} - y^{2} = (x+y)(x-y) = 8 	imes 2 = 16$.

If $x + y = 8$ and $xy = 15$, find $x^{2} - y^{2}$ given $x > y$.