Question

if x^2+1/x^2=14. find value of x^3+1/x^3​

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 14 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16 \\ \\ (x + \frac{1}{x} ) ^{2} = {4}^{2} \\ \\ x + \frac{1}{x} = 2 \\ \\ x + \frac{1}{x} = - 4$

${x}^{3} + \frac{1}{ {x}^{3} } = (x + \frac{1}{x} )^{3} - 3(x + \frac{1}{x} ) \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 52 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = - 52$

hope it helps