Question

if x=3+ square root 8 then find the value of x^2+1/x^2. GIVE PROPER STEPS PLEASE

Answer 1

$i) x = 3 + \sqrt{8} \: --(1) \:(given)$

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

$iii ) x + \frac{1}{x} \\= 3 + \sqrt{8} + 3 - \sqrt{8}\\= 6\: --(3)$

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

Therefore.,

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

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