Question

if x = √3 - √2, then find the value of (x - 1/x)^2
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Answer 1

ANSWER :–

GIVEN :–

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

TO FIND :–

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

SOLUTION :–

● FIRST WE HAVE TO FIND (1/X)

${ \bold{ = > \: \: \frac{1}{x} = \frac{1}{ \sqrt{3} - \sqrt{2} } }} \\ \\ { \bold{ = > \: \: \frac{1}{x} = \frac{1}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } }} \\ \\ { \bold{ = > \frac{1}{x} = \frac{ \sqrt{3} + \sqrt{2} }{3 - 2} = \sqrt{3} + \sqrt{2} }}$

● NOW WE HAVE TO FIND –

${ \bold{ { = > (x - \frac{1}{x}) }^{2} = {( \sqrt{3} - \sqrt{2} - \sqrt{3} - \sqrt{2} ) }^{2} }} \\ \\ { \bold{ = > {(x - \frac{1}{x} )}^{2} = {( - 2 \sqrt{2} )}^{2} = 4 \times 2 = 8 }}$