Question

(a) If x+ 1/x= 3, then find x^3+1/x^3​

Answer 1

this will help you

this method is also used in calculating X^4 + 1/X^4 for also

Answer 2

given :

$x \times + \frac{1}{x} = 3$

To find :

${x}^{3} + \frac{1}{ {x}^{3} } = \: ?$

sol: Take cube to both sides of one equation

$= (x + \frac{1}{x} ) {}^{3} = (3) {}^{3} \\ = x {}^{3} + \frac{1}{x {}^{3} } + 3x + \frac{1}{x} \\ = \: (x + \frac{1}{x} ) = (a + b) {}^{3} = a {}^{3} + b {}^{3} = 3ab \: (a + b) \\ = x {}^{3} + \frac{1}{x {}^{3} } + 3 \: (3) = 27 \: \: \: \: ( x = \frac{1}{x} = 3) \\ = x {}^{3} + \frac{1}{x {}^{3 } } = 27 - 9 \\ = x {}^{3} + \frac{1}{x {}^{3} } = 18$

I hope this may help you