Question

If x-1/x=4 then find the value of x²+1/x² and x⁴+1/x⁴

Answer 1

$Given \: x - \frac{1}{x} = 4 \: --(1)$

$i ) Value \:of \:x^{2} + \frac{1}{x^{2}} \\= \Big( x - \frac{1}{x}\Big)^{2} + 2 \times x \times \frac{1}{x} \\= 4^{2} + 2 \: [ From \:(1) ] \\= 16 + 2 \\= 18\: --(2)$

$ii ) Value \: of \: x^{4} + \frac{1}{x^{4}} \\= \Big( x^{2} + \frac{1}{x^{2}} \Big)^{2} - 2 \times x^{2} \times \frac{1}{x^{2}} \\= 18^{2} - 2 \: [ From \: (2) ] \\= 328 - 2 \\= 326$

Therefore.,

$\red { Value \:of \:x^{2} + \frac{1}{x^{2}}} \green { = 18 }$

$\red { Value \:of \:x^{4} + \frac{1}{x^{4}}} \green { = 326 }$

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Answer 2

Answer:

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