Question

if x^3+1/x^3=18 then find x^5+1/x^5?

Answer 1

${x}^{3} + \frac{1}{ {x}^{3} } = 18$



$\textbf{Square on both sides, }$





${({x}^{3} + \frac{1}{ {x}^{3} } ) }^{2} = {18}^{2} \\ \\ \\ = > {x}^{3 + 2} + \frac{1}{ {x}^{3 + 2} } + 2( {x}^{3} \times \frac{1}{ {x}^{3} } ) = 324 \\ \\ \\ = > {x}^{5} + \frac{1}{ {x}^{5} } + 2 = 324 \\ \\ \\ = > {x}^{5} + \frac{1}{ {x}^{5} } = 324 - 2 \\ \\ \\ = > {x}^{5} + \frac{1}{ {x}^{5} } = 322$