Question

Very important please answer ​

Answer 1

$\boxed{\huge{\red{Explaination}}}$

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$\huge{\blue{\underline{Given:}}}$

$x + \frac{1}{x} = 2 \\ {x}^{2} + 1 = 2x \\ {x}^{2} - 2x + 1 = 0 \\ {x}^{2} - x - x + 1 = 0 \\ x(x - 1) - 1(x - 1) = 0 \\ x = 1$

$\huge{\underline{To\:find:}}$

$= {x}^{4} + \frac{1}{ {x}^{4} } \\ = 1 + \frac{1}{1} \\ = 1 + 1 \\ = 2$

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Answer 2

$\left ( x^{4} +1/x^{4}\right )=34$

Step-by-step explanation:

Given,

$\left ( x-1/x \right )=2$

$\left ( x^{4}+1/x^{4} \right )=?$

Solution,

$\left ( x-1/x \right )=2$

Squaring both side

$\left ( x-1/x \right )^{2}=2^{2}$

$x^{2}+1/x^{2}-2\times x/x=4$         $\left ( \left ( a-b \right )^{2} =a^{2}+b^{2}-2ab\right )$

$x^{2}+1/x^{2}=4+2=6$             (1)

Squaring equation 1 both side

$\left ( x^{2}+1/x^{2} \right )^{2}=6^{2}$                      

$x^{4}+1/x^{4}+2\times x^{2}/x^{2}=36$        $\left ( \left ( a+b \right )^{2} =a^{2}+b^{2}+2ab\right )$

$x^{4}+1/x^{4}+2=36$

$\left ( x^{4}+1/x^{4} \right )=36-2=34$

$\left ( x^{4} +1/x^{4}\right )=34$