Question

Solve the following equation.
$x+y-\sqrt{xy}=6,x^2+y^2+xy=84$.

Answer 1

$x^2+xy+y^2=84$......(1), $x+y-\sqrt{xy}=6$.....(2)

$x^2+y^2+xy+xy-xy=84$

$(x+y{)}^2-xy=84$.....(3)

From equation $2$

$x+y=6+\sqrt{xy}$

$(6+\sqrt{xy}{)}^2-xy=84$

$36+12\sqrt{xy}+xy-xy=84$

$\sqrt{xy}=4$

$xy=16$