Question

please solve x^2+1/x^2=8, find x^3+1/x^3

Answer 1

Answer:

${x}^{2} + \frac{1}{ {x}^{2} } = 8 \\ adding \: 2 \: on \: both \: sides \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 8 + 2 \\ {(x + \frac{1}{x}) = 10 }^{2} \\ x + \frac{1}{x} = \sqrt{10} \\ cubing \: both \: sides \\ {(x + \frac{1}{x}) }^{3} = 10 \sqrt{10} \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times x \times \frac{1}{x} \times x + \frac{1}{x} ) = 10 \sqrt{10} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times \sqrt{10} = 10 \sqrt{10} \\ {x}^{3} + \frac{1}{ {x}^{3} } = 7 \sqrt{10 }$