Question

Solve this if you can

Answer 1

Answer:

2

Step-by-step explanation:

Given that, $x =\sqrt{\frac{\sqrt{2} +1}{\sqrt{2}-1 } }$

                  $x =\sqrt{\frac{\sqrt{2} +1}{\sqrt{2}-1 } *\frac{\sqrt{2} +1}{\sqrt{2}+1}$

                  $x= \sqrt{\frac{(\sqrt{2}+1) ^{2} }{2 -1} }$

                  $x = \sqrt{2} +1$

Now,   $\frac{x^{2}-1 }{x} = \frac{(\sqrt{2} +1)^{2} -1}{\sqrt{2} +1}$

                    $= \frac{2+1+2\sqrt{2} -1}{\sqrt{2} +1}$

                    $= \frac{2+2\sqrt{2} }{\sqrt{2} +1}$

                     $= 2.$