Question

If x = 3 - 2 √2 find : x²+1/x²
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Answer 1

Step-by-step explanation:

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Answer 2

Given :

• x = 3 - 2√2

To find :

• x² + 1/x²

According to the question,

$\implies\sf{ \dfrac{1}{x} = \dfrac{1}{3 - 2 \sqrt{2} } \times \dfrac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } } \\ \\ \sf \implies{ \dfrac{3 + 2 \sqrt{2} }{9 - 8} } \\ \\ \implies \sf{3 + 2 \sqrt{2} } \: \green \bigstar$

$\implies\sf{x + \dfrac{1}{x} } \\ \\ \implies \sf{3 - \cancel{ 2 \sqrt{2} }+ 3 + \cancel{ 2 \sqrt{2} } } \\ \\ \implies \sf{6}$

Squaring on both sides :

$\implies\sf{ {x}^{2} + \dfrac{1}{x {}^{2} } = {6}^{2} } \\ \\ \implies \sf{ {x}^{2} + \dfrac{1}{ {x}^{2} } + 2 \times x \times \dfrac{1}{x} = 36 } \\ \\ \implies \sf{x {}^{2} + \frac{1}{ {x}^{2} } = 36 - 2} \\ \\ \implies \sf{ {x}^{2} + \dfrac{1}{ {x}^{2} } = 34 } \green \bigstar$