Question

if x+1/x= 3 find the value of x⁴+1/x⁴​

Answer 1

Answer:

${x}^{4} + \frac{1}{ {x}^{4} } = 40$

Step-by-step explanation:

Given that:

$x + \frac{1}{x} = 3$

To find:

$the \: value \: of \: {x}^{4} + \frac{1}{ {x}^{4} }$

Solution:

Squaring on both sides,we get

$( {x}^{2} + \frac{1}{ {x}^{2} } ) = {3}^{2} \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 7$

Again, squaring on both sides, we get

$( {x}^{2} + \frac{1}{ {x}^{2} } ) ^{2} = ({7})^{2} \\ = > {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 42 \\ = > {x}^{4} + \frac{1}{ {x}^{4} } = 42 - 2 \\ = > {x}^{4} + \frac{1}{ {x}^{4} } = 40 \: ans.$