Question

If x+1/x=√3, find the value of x³+1/x³

Answer 1

Step-by-step explanation:

Given that:-

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

Find:-

${x}^{3} + \frac{1}{ {x}^{3} } = what$

Solution:-

doing cube root both side:-

$\: \: \: \: \: \: \: \: \: \: {(x + \frac{1}{x}) }^{3} = \sqrt{3 } \\ = > {x}^{3} + \frac{1}{ {x}^{3} } + 3.x. \frac{1}{x} (x + \frac{1}{x} ) \: = { \: (\sqrt{3} }) \: ^{3} \\ = > {x}^{3} + \frac{1}{ {x}^{3} } + 3. \sqrt{3} = 3 \\ = > {x}^{3} + \frac{1}{ {x}^{3} } = 3 - 3 \sqrt{3} \\ = > {x}^{?} + \frac{1}{ {x}^{3} } = 3(1 - \sqrt{3 } )$