[tex] \sqrt{x+1}- \sqrt{x-1}= \sqrt{2} \\ DVA:x \geq 1 \\ ( \sqrt{x+1}- \sqrt{x-1})^2=( \sqrt{2})^2 \\ x+1+x-1-2 \sqrt{(x+1)(x-1}=2 \\ -2 \sqrt{ x^{2} -1} =2-2x \\ \sqrt{ x^{2} -1}=x-1 \\x \geq 1 \\ ( \sqrt{x^2-1})^2=(x-1)^2 \\ x^{2} -1= x^{2} -2x+1 \\ 2x=2 \\ x=1 [/tex]
