Give the algebraic proof that the square root of A^2+B^2= A+B, then either A=0 or B=0

Question

I'm having trouble getting the algebraic proof for this equation and understanding the problem.

Answer 1

$\sqrt{A^2+B^2}=A+B$

Square both sides.

$A^2+B^2=(A+B{)}^2$

Carry out the expansion on the right side of the equation:

A^2+B^2=A^2+2AB+B^2

Since A^2 and B^2 appear on both sides, they cancel each other out.

Therefore 0=2AB or 0=AB.

Either A=0 or B=0 for a non-trivial solution. The trivial solution also satisfies the original equation (A and B both equal 0).