Question

Given that x - y = a and xy = b , show that x^2 + y^2 = a^2 + 2b .

Answer 1

Hello,

$x-y=a ==\textgreater \ (x-y)^2=a^2 \ ==\textgreater \ x^2-2xy+y^2=a^2\\\\ xy=b\ ==\textgreater\ 2xy=2b\\\\ x^2-2xy+b^2+2xy=a^2+2b==\textgreater\ x^2+y^2=a^2+2b$