Math, asked by shivangigite7006, 10 months ago

If the x=(3+2√2)find value x^2+1/x^2

Answers

Answered by mysticd
0

 Given \: x = (3+2\sqrt{2}) \: --(1)

 \frac{1}{x} = \frac{1}{(3+2\sqrt{2})}\\= \frac{(3-2\sqrt{2})}{(3+2\sqrt{2})(3-2\sqrt{2})}\\=</p><p> \frac{(3- 2\sqrt{2})}{3^{2} - (2\sqrt{2})^{2} } \\= \frac{(3-2\sqrt{2})}{9 - 8} \\= \frac{(3-2\sqrt{2})}{1}\\= (3-2\sqrt{2})\: --(2)

 x + \frac{1}{x} \\= 3+2\sqrt{2} + 3-2\sqrt{2}\\= 6 \: --(3)

 Now, x^{2} + \frac{1}{x^{2}} = \Big( x + \frac{1}{x}\Big)^{2} - 2 \times x \frac{1}{x} \\= 6^{2} - 2 \\= 36 - 2 \\= 34

Therefore.,

 \red { Value \:of \: x^{2} + \frac{1}{x^{2}} } \green {= 34 }

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