Question

(x+1/x) =9 find the value of x^4+1/x^4​

Answer 1

Answer:

${x}^{4} + \frac{1}{ {x}^{4} } = 6239$

Step-by-step explanation:

$x + \frac{1}{x} = 9 \\ \\ {(x + \frac{1}{x} )}^{2} = {9}^{2} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 81 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 81 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 79 \\ \\ {( {x}^{2} + \frac{1}{ {x}^{2} } )}^{2} = {79}^{2} \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 6241 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 6241 - 2 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 6239$