Question

Rezolvati in multimea nr reale ecuatia √x+1 - √x-1 = √2

Answer 1

$\sqrt{x+1}- \sqrt{x-1}= \sqrt{2} \\ x \geq 1 \\ x+1+x-1-2 \sqrt{x^2-1} =2 \\ -2 \sqrt{x^2-1}=2-2x/:(-2 )\\ \sqrt{x^2-1}=x-1 \\ x^{2} -1= x^{2} -2x+1 \\ -2=-2x \\ x=1$