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Prove that x-y = √(x+y)^2-4xy?

2 Answers

4 votes

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

User Bubersson
by
9.1k points
3 votes

Proved Below


\Longrightarrow x-y = √((x+y)^2-4xy)


\Longrightarrow x-y = √(x^2+2(x)(y)+ y^2-4xy)


\Longrightarrow x-y = √(x^2+2xy-4xy+y^2)


\Longrightarrow x-y = √(x^2-2xy+y^2)


\Longrightarrow x-y = √((x-y)^2)


\Longrightarrow x-y =x-y

User UkFLSUI
by
8.0k points

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