Question

uIf (x+1/x)=5 then Find (i)x²+1/x²(ii) x⁴+1/x⁴​

Answer 1

$Given \: x + \frac{1}{x} = 5 \:---(1)$

$i ) Value \: of \: x^{2} + \frac{1}{x^{2}}$

$= \Big( x + \frac{1}{x}\Big)^{2} - 2$

$= 5^{2} - 2 \: [ From \: (1) ]$

$= 25 - 2$

$= 23\: --(2)$

$ii) Value \: of \: x^{4} + \frac{1}{x^{4}}$

$= \Big( x^{2} + \frac{1}{x^{2}}\Big)^{2} - 2$

$= 23^{2} - 2 \: [ From \: (2) ]$

$= 529 - 2$

$= 527\: --(3)$

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