Question

If $\sqrt{m}+\sqrt{n}-\sqrt{p}=0,$ then prove that $(m+n-p{)}^2=4mn$

Answer 1

Given $\sqrt{m}+\sqrt{n}-\sqrt{p}=0$

$⟹\sqrt{m}+\sqrt{n}=\sqrt{p}$

Squaring on both sides

$(\sqrt{m}+\sqrt{n}{)}^2=(\sqrt{p}{)}^2$

$m+n+2\sqrt{mn}=p$

$m+n-p=-2\sqrt{mn}$

Squaring on both sides

$(m+n-p{)}^2=4mn$