An algebra problem by Mark Dave Martin

$x^2-xy+y^2=19$ $\implies$ $x^2+y^2=19+xy$ $\implies$ $13-19=xy$ $\implies$ $-6=xy$ $\implies$ $\color{#D61F06}\boxed{36=x^2y^2}$

The given eq is x^2 + y^2 = 13

And other eq is x^2 - xy + y^2 = 19 => (x^2 + y^2) - xy = 19 => 13 - xy = 19 => xy = 19 - 13 => xy = 6 => (xy)^2 = 6^2 => x^2.y^2 ===--> 35

Subsituting values we get -xy =6 so sqaring both side we get answer 36. K.K.GARG,India

Hello and peace be upon you,

as x^2 + y^2 = 13 ,

by 13 - xy = 19 ,

xy = - 6 , by squaring both sides,

(xy) ^ 2 = x^2y^2 = (-6)^2 = 36...

thanks....