Question

If x square + 1 by x square is equal to 47 then find the x cube + 1 by x cube

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 47 \\ {(x + \frac{1}{x} )}^{2} - 2 = 47 \\ x + \frac{1}{x} = \sqrt{49} = 7 \: \: or \: \: - 7$
${x}^{3} + \frac{1}{ {x}^{3} } = {(x + \frac{1}{x} )}^{3} - 3(x + \frac{1}{x} ) \\ = {7}^{3} - 3 \times 7 \: \: or \: \: {( - 7)}^{3} - 3 \times - 7 \\ = 322 \: \: or \: \: - 322$