Question

If x= sqrt2+1/ sqrt2-1, then find 1/x^2
pls answer fast (urgent)

Answer 1

Answer:

x=$3+2\sqrt{2}$

Step-by-step explanation:

Given:-

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

To Find:-

$\frac{1}{x^{2} }$

Solution:-

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

Rationalising The Denominator:-

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

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

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

x=$3+2\sqrt{2}$