Question

Prove that x-y = √(x+y)^2-4xy?

Answer 1

Let's check

x-y=√(x+y)²-4xy

Solve RHS

• √(x+y)²-4xy
• √x²+2xy+y²-4xy
• √x²+y²-2xy
• √(x-y)²
• x-y

Hence proved

Answer 2

Proved Below

$\Longrightarrow x-y = \sqrt{(x+y)^2-4xy}$

$\Longrightarrow x-y = \sqrt{x^2+2(x)(y)+ y^2-4xy}$

$\Longrightarrow x-y = \sqrt{x^2+2xy-4xy+y^2}$

$\Longrightarrow x-y = \sqrt{x^2-2xy+y^2}$

$\Longrightarrow x-y = \sqrt{(x-y)^2}$

$\Longrightarrow x-y =x-y$