Question

x^2+1/x^2=23 find x^4+1/x^4

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 23$



Square on both sides,



$= \: > {( {x}^{2} + \frac{1}{ {x}^{2} } )}^{2} = {(23)}^{2} \\ \\ \\ \\ = \: > {x}^{4} + \frac{1}{ {x}^{4} } + 2( {x}^{2} \times \frac{1}{ {x}^{2} } ) = 529 \\ \\ \\ \\ = \: > {x}^{4} + \frac{1}{ {x}^{4} } + 2(1) = 529 \\ \\ \\ \\ = \: > {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 529 \\ \\ \\ \\ = \: > {x}^{4} + \frac{1}{ {x}^{4} } = 529 - 2 \\ \\ \\ \\ = \: > {x}^{4} + \frac{1}{ {x}^{4} } = 527$