Question

If a=2-root2 ,find (a-1/a)square

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{{(a - \frac{1}{a}) }^{2}=1.27}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies a = 2 - \sqrt{2} \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies (a - \frac{1}{a} )^{2} = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt \circ \: {(x- y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = {a}^{2} + (\frac{1}{a })^{2} - 2 \times a \times \frac{1}{a} \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = ({2 - \sqrt{2} })^{2} + (\frac{1}{2 - \sqrt{2} } )^{2} - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = {2}^{2} + ({ \sqrt{2} })^{2} - 4 \sqrt{2} + \frac{1}{ {2}^{2} + (\sqrt{2})^{2} - 4 \sqrt{2} } - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} =4 + 2 - 4 \sqrt{2} + \frac{1}{4 + 2 - 4 \sqrt{2} } - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = 6 - 4 \sqrt{2} + \frac{1}{6 - 4 \sqrt{2} } \times \frac{6 + 4 \sqrt{2} }{6 + 4 \sqrt{2} } - 2$

$\tt: \implies {(a - \frac{1}{a}) }^{2} =6 - 4 \sqrt{2} + \frac{6 + 4 \sqrt{2} }{ 36 - 32 } - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} =6 - 4 \sqrt{2} + \frac{6 + 4 \sqrt{2} }{4} - 2 \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = \frac{24 - 16 \sqrt{2} + 6+4 \sqrt{2} - 8 }{4} \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = \frac{22 - 12 \sqrt{2} }{4} \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = \frac{11 - 6\sqrt{2} }{2} \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = \frac{11 - 6\times 1.41}{2} \\ \\ \tt: \implies {(a - \frac{1}{a}) }^{2} = \frac{2.54}{2} \\ \\ \green{\tt: \implies {(a - \frac{1}{a}) }^{2} = 1.27}$