Question

if x = 1+√2. Then find value of (x–1/x)²​

Answer 1

Answer:

4

Step-by-step explanation:

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

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

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

${(x - \frac{1}{x}) }^{2} = {( 1 + \sqrt{2} - ( \sqrt{2} - 1)}^{2} = {(1 + \sqrt{2} - \sqrt{2} + 1)}^{2} = {2}^{2} = 4$