Question

X = 1-✓2 find the value of x+1/x
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Answer 1

Step-by-step explanation:

Given:-

x = 1-√2

Solution:-

\begin{gathered} \sf \: x = 1 - \sqrt{2} \\ \\ \therefore \sf \: x - \frac{1}{x} = (1 - \sqrt{2} ) - \frac{1}{(1 - \sqrt{2}) } \\ \\ \sf \implies \: (1 - \sqrt{2} ) - \frac{1}{(1 - \sqrt{2}) } \times \frac{(1 + \sqrt{2}) }{(1 + \sqrt{2}) } \\ \\ \sf \implies \: (1 - \sqrt{2} ) - \frac{(1 + \sqrt{2} )}{ {(1)}^{2} - {( \sqrt{2} )}^{2} } \\ \\ \sf \implies \: 1 - \sqrt{2} - \frac{1 + \sqrt{2} }{1 - 2} \\ \\ \sf \implies \: (1 - \sqrt{2} ) - ( - 1 + \sqrt{2} ) \\ \\ \sf \implies \: 1 - \sqrt{2} + 1 + \sqrt{2} \\ \\ \sf \implies \: 1 + 1 \\ \\ \sf \implies \: 2 \\ \\ \sf \therefore \: { \left(x - \frac{1}{x}\right ) }^{4} = {(2)}^{4} = 16\end{gathered}x=1−2∴x−x1=(1−2)−(1−2)1⟹(1−2)−(1−2)1×(1+2)(1+2)⟹(1−2)−(1)2−(2)2(1+2)⟹1−2−1−21+2⟹(1−2)−(−1+2)⟹1−2+1+2⟹1+1⟹2∴(x−x1)4=(2)4=16