Question

if x minus one upon X equal to 3 + 2 root 2 find the value of x cube minus one up on x cube

Answer 1

$x - \frac{1}{x} = 3 + 2 \sqrt{2} \\ on \: cubing \: \: we \: get \\ (x - \frac{1}{x} ) ^{3} = (3 + 2 \sqrt{2} )^{3} \\ {x}^{3} - \frac{1}{x ^{3} } + 3( {x})^{2} ( \frac{ - 1}{x} ) + 3(x)( \frac{ - 1}{x} ) ^{2} = ({3})^{3} + (2 \sqrt{2} )^{3} + 3( {3})^{2} (2 \sqrt{2} ) + 3(3)(2 \sqrt{2} ) ^{2} \\ {x}^{3} - \frac{1}{x ^{3} } - 3x + \frac{3}{x} = 27 + 16 \sqrt{2} + 54 \sqrt{2} + 48 \\ {x}^{3} - \frac{ 1}{x^{3} } - 3(x - \frac{1}{x} ) = 75 + 70 \sqrt{2} \\ {x}^{3} - \frac{ 1}{x^{3} } - 3(3 + 2 \sqrt{2} ) = 75 + 70 \sqrt{2} \\ {x}^{3} - \frac{ 1}{x^{3} } - 9 - 6 \sqrt{2} = 75 + 70 \sqrt{2} \\ {x}^{3} - \frac{ 1}{x^{3} } = 75 + 70 \sqrt{2} + 9 + 6 \sqrt{2} \\ {x}^{3} - \frac{ 1}{x^{3} } = 84 + 76 \sqrt{2}$

Answer 2

HELLO ,
May this answer help you