[tex] \sqrt{x+1}- \sqrt{x-1} = \sqrt{2}\\
[/tex]
Conditiile de existanta a radicalilor:
x + 1 ≥ 0 ==> x ∈ [-1, ∞)
x - 1 ≥ 0 ==> x ∈ [1, ∞)
Intersectia: x ∈ [1, ∞)
Ridicam la patrat ecuatia:
[tex](x+1)-2 \sqrt{(x+1)(x-1)}+(x-1)=2 \\
2x-2 \sqrt{x^2-1}=2\\
\sqrt{x^2-1}=x-1 [/tex]
Ridicam din nou la patrat:
[tex]x^2-1=x^2-2x+1\\
2x=2\\
x=1[/tex]
