If-z-1-2-x-1-2-y-1-2-Prove-that-x-y-z-2-4xy-

Question Number 109396 by ZiYangLee last updated on 23/Aug/20

If z^{\frac{1}{2}} = x^{\frac{1}{2}} + y^{\frac{1}{2}}

Prove that {(x + y - z)}^{2} = 4 x y

Answered by bemath last updated on 23/Aug/20

z = x + y + 2 \sqrt{x y}

2 \sqrt{x y} = z - (x + y)

{(2 \sqrt{x y})}^{2} = {(z - (x + y))}^{2} = {((x + y) - z)}^{2}

4 x y = {(x + y - z)}^{2}

Commented by Rasheed.Sindhi last updated on 23/Aug/20

\in \times \subset\in∣∣\in \cap ⊤!

Commented by ZiYangLee last updated on 23/Aug/20

Yay!