Question

X=√2+1, then find x^2+1/x^2

Answer 1

Answer:

$x = \sqrt{2} + 1$

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

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

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

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

now,

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

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

have to find out,

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

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

$= ({2 \sqrt{2}) }^{2} - 2$

$= 8 - 2$

$= 6$