Question

If x^2+1/x^2= 34, find x^3+1/x^3​

Answer 1

$\huge \bold {\red {\underline {\underline{Answer!}}}}$

$\star \: \: {\blue{\underline {Solution}}} \blue{:-}$

${x}^{2} + \frac{1}{ {x}^{2} } = 34 \\ \longrightarrow {(x + \frac{1}{x} )}^{2} - 2x \frac{1}{x} = 34 \\ \longrightarrow{(x + \frac{1}{x} )} = \sqrt{36} \\ \longrightarrow {(x + \frac{1}{x} )}^{3} = {6}^{3} \\ \longrightarrow {x}^{3} + \frac{1}{ {x}^{3} } + 3x \frac{1}{x} (x + \frac{1}{x} ) = 216 \\ \longrightarrow {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 6 = 216 \\ \longrightarrow \boxed{{x}^{3} + \frac{1}{ {x}^{3} } = 198}$

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