Question

$if \: a = \sqrt{2 } + 1 \: find \: (a - 1/a) {}^{2}$
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Answer 1

Step-by-step explanation:

$\sf{ \because{a = \sqrt{2} + 1}}$

$\sf{ \therefore \: \frac{1}{a} = \frac{1 }{ \sqrt{2} + 1 } }$

$\sf \: On \: rationalise \: the \: denominator$

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

$\sf \: = \frac{ \sqrt{2} - 1}{ {( \sqrt{2} )}^{2} - {1}^{2} }$

$\sf \: = \frac{ \sqrt{2} - 1}{2 - 1}$

$\sf \: = \sqrt{2} - 1$

$\sf \: Now, \: a - \frac{1}{a} = \sqrt{2} + 1 - ( \sqrt{2} - 1)$

$\sf \: = \sqrt{2} + 1 - \sqrt{2} + 1$

$\sf = \: 1 + 1 + \sqrt{2} - \sqrt{2}$

$\sf \: = 2$

I hope it is helpful

Answer 2

Answer:

$if \: a = \sqrt{2 } + 1 \: find \: (a - 1/a) {}^{2}$ is the correct amswer

Step-by-step explanation:

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