Question

if m+1/m=√3 find:- m^3+1/m^3

Answer 1

Is the answer 3root3???

If yes I will edit the answer and write it

Answer 2

${m} + ( \frac{1}{m} ) = \sqrt{3}$

We know

(a+b)³=a³+b³+3a2b+3ab²

$(m + \frac{1}{m} ) {}^{3} = {m}^{3} + \frac{1}{ {m}^{3} } + 3 \times {m}^{2} \times \frac{1}{m} + 3 \times m \times \frac{1}{ {m}^{2} } \\ \\ ( \sqrt{3} ) {}^{3} = ( {m}^{3} + \frac{1}{ {m}^{3} } ) + 3m + \frac{3}{m} \\ \\ 3 \sqrt{3} = ( {m}^{3} + \frac{1}{ {m}^{3} } ) + 3(m + \frac{1}{m} ) \\ \\ 3 \sqrt{3} = ( {m}^{3} + \frac{1}{ {m}^{3} } ) + 3 \sqrt{3} \\ \\ {m}^{3} + \frac{1}{ {m}^{3} } = 3 \sqrt{3} - 3 \sqrt{3} = 0$

$\boxed{\mathbf{\huge{ {m}^{3} + \frac{1}{ {m}^{3} } =0}}}$