Question

find the value of x³-1/x³ if (x-1/x)=5,x²+1/x²=2​

Answer 1

$as \: we \: know \\ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) \\ a = x \: and \: b = \frac{1}{x} \\ {x}^{} - \frac{1}{ {x}^{3} } = (x - \frac{1}{x} )( {x}^{2} + x \times \frac{1}{x} + \frac{1}{ {x}^{2} } ) \\ = 5 \times (2 + 1) \\ = 5 \times 3 = 15$

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