Question

If x + 1 by x =

5, find the value of x cube + 1 by x cube​

Answer 1

$</p><p></p><p>\bold{\underline{\sf Given:}} </p><p>\\ </p><p> \sf \rightarrow \quad x + \frac{1}{x} = 5 </p><p></p><p>\\ \\</p><p>$

$</p><p></p><p>\bold{\underline{\sf To Find:}} </p><p>\\ </p><p> \sf \rightarrow \quad x^{3} + \frac{1}{x^{3}} = ? \\ \\</p><p></p><p>$

$</p><p></p><p>\bold{\underline{\sf Solution:}} </p><p>\\ </p><p>\\</p><p>$

$</p><p> \sf \rightarrow \quad x + \frac{1}{x} = 5 \\ \\ \sf \rightarrow \quad \bigg(x + \frac{1}{x} \bigg)^{3} = {(5)}^{3} \\ \\ \sf \quad (a + b)^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ \\ \sf \rightarrow \quad {x}^{3} + \frac{1}{ {x}^{3} } + 3 \cdot \cancel{x} \cdot \frac{1}{ \cancel{x}} \left(x + \frac{1}{x} \right) = 125 \\ \\ \sf \rightarrow \quad {x}^{3} + \frac{1}{ {x}^{3} } = 125 - 3 \\ \\ \sf \rightarrow \quad {x}^{3} + \frac{1}{ {x}^{3} } = 122</p><p>$