Question

find x cube + 1 over x cube if X + 1 over x is equal to 3 ​

Answer 1

Hey

$Given: \: \: x + \frac{1}{x} = 3 \\ \\ To \: find:\: \: (x {}^{ 3} + \frac{1}{x {}^{3} } ) \\ \\ Now, \\ (x + \frac{1}{x} ) {}^{3} = x {}^{3} + \frac{1}{x {}^{3} } + 3(x + \frac{1}{x} ) \\ \\ = > 3 {}^{3} = x {}^{3} + \frac{1}{x {}^{3} } + 3(3) \\ \\ = > x {}^{3} + \frac{1}{x {}^{3} } = 27 - 9 = 18$