Question

x-1/x=3 find x×x×x-1/x×x×x

Answer 1

Hii
Nice question

Question:-

x - 1/x = 3
Then x³ - 1/x³ = ?

Solution:-

First we find x² + 1/x²

$({x - \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \times x \times \frac{1}{x} \\ {3}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 9 + 2 = 11 \\ \\ coming \: back \: to \: our \: question \\ {x}^{3} - \frac{1}{ {x}^{3} } = (x - \frac{1}{x} )( {x}^{2} + \frac{1}{ {x}^{2} } - x \times \frac{1}{x} )\\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = (3)(11 - 1 ) \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = 3 \times 10 \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = 30$

Hope this helps you.