Question

xsquare×1/xsquare=11 find xcube-1/xcube

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 11$
subtracting 2 on both sides
${x}^{2} + \frac{1}{ {x}^{2} } - 2 = 9$
${x}^{2} + \frac{1}{ {x}^{2} } - 2 \times x \times \frac{1}{x} = 9$
of x = a and 1/x =b then
${a}^{2} + {b}^{2} - 2ab = {(a - b)}^{2}$
${( {x} - \frac{1}{x} )}^{2} = 9 \\ x - \frac{1}{x} = 3$
${(x - \frac{1}{x})}^{3} = 27$
${x}^{3} - {\frac{1}{x} }^{3} - 3 \times x \times \frac{1}{x} (x - \frac{1}{x} ) = 27$
${x}^{3} - { (\frac{1}{x}) }^{3} - 3(3) = 27$
${x}^{3} - {(\frac{1}{x})}^{3} = 36$
Hence the answer is 36.
Hope it helps and if possible then please mark it as the brainliest answer.