Question

If x- 1/x=3 then find the value of x^4+1/x^4

Answer 1

Step-by-step explanation:

$x - \frac{1}{x} = 3 \\ on \: squaring \: both \: sides \\ {(x - \frac{1}{x}) }^{2} = {(3)}^{2} \\ = > {x}^{2} + { \frac{1}{x} }^{2} - 2 = 9 \\ = > {x}^{2} + { \frac{1}{x} }^{2} = 9 + 2 \\ = > {x}^{2} + { \frac{1}{x} }^{2} = 11\\ \\ again \: squaring \: both \: side \\ {( {x}^{2} + { \frac{1}{x} }^{2}) }^{2} = {(11)}^{2} \\ = > {x}^{4} + { \frac{1}{x} }^{4} + 2 = 121 \\ = > {x}^{4} + { \frac{1}{x} }^{4} = 121 - 2 \\ = > {x}^{4} + { \frac{1}{x} }^{4} = 119$

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