Question

If x = √2 + 1 , find the value of (x - 1/x)² .

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Answer 1

4

Step-by-step explanation:

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

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

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

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

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

(√2 + 1 - (√2 -1))²

(√2 + 1 - √2 + 1)²

(2)²

= 4