Question

Fimd the value of x sq +1/x sq. Wjen x sq. Is 4 +√15

Answer 1

$Given \: x = 4 + \sqrt{15} \: --(1)$

$i) \frac{1}{x} = \frac{1}{(4+\sqrt{15})}\\= \frac{(4 - \sqrt{15})}{(4 + \sqrt{15})(4 -\sqrt{15} )} \\= \frac{(4 - \sqrt{15})}{(4^{2} -(\sqrt{15} )^{2}} \\= \frac{(4 - \sqrt{15})}{16 - 15 } \\= \frac{(4 - \sqrt{15})}{1} \\= 4-\sqrt{15} \: ---(2)$

$ii ) x + \frac{1}{x} \\= 4 + \sqrt{15}+4 - \sqrt{15}\\= 8 \: --(2)$

$x^{2} + \frac{1}{x^{2}} = \Big( x + \frac{1}{x}\Big)^{2} - 2 \times x\times \frac{1}{x} \\= \Big( x + \frac{1}{x}\Big)^{2} - 2 \\= 8^{2} - 2 \\= 64 - 2 \\= 62$

Therefore.,

$\red { Value \:of \:x^{2} + \frac{1}{x^{2}} }\green {= 62 }$

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Answer 2

Don't kow.... ............. ..................