Question

x⁴ +1/x⁴=6239 find (x+1/x)=?​

Answer 1

$\bf\large\underline\blue{Question:-}$

• ${x}^{4} + \frac{1}{ {x}^{4} } = 6239$, find the value of
• $x + \frac{1}{x}$

$\bf\large\underline\blue{Solution:-}$

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

$\implies {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 6239 + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} }$

$\implies ({x}^{2} + \frac{1}{ {x}^{2} } )^{2} = 6241$

$\implies ({x}^{2} + \frac{1}{ {x}^{2} } ) = \sqrt{6241}$

$\implies ({x}^{2} + \frac{1}{ {x}^{2} } ) = 79$

$\implies ({x}^{2} + \frac{1}{ {x}^{2} } ) + 2 \times x \times \frac{1}{x} = 79 + 2 \times x \times \frac{1}{x}$

$\implies {(x + \frac{1}{x} )}^{2} = 81$

$\implies {(x + \frac{1}{x} )} = \sqrt{81}$

$\implies {(x + \frac{1}{x} )} = \pm9$

$\bf\large\underline\blue{Answer:-}$

• $x + \frac{1}{x} = \pm9$