Question

If x+1/x=√3 find x^3+1/x^3

Answer 1

GIVEN...

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

TO FIND...

$= > the \: value \: of \: \: x ^{3} + \frac{1}{x ^{3} }$

IDENTITY USED...

$= >( x + y) ^{3} = x ^{3} + y ^{3} + 3xy(x+y)</p><p></p><h3>SOLUTION...</h3><p></p><p>[tex] = > x + \frac{1}{3} = \sqrt{3} \\ \\ by \: cubing \: both \: sides....... \\ \\ = > (x + \frac{1}{x} ) ^{3} = ( \sqrt{3} ) ^{3} \\ \\ = > x ^{3} + \frac{1}{x ^{3} } + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 3 \times \sqrt{3} \\ \\ = > x ^{3} + \frac{1}{x^{3} } + 3(x + \frac{1}{x} ) = 3 \sqrt{3} \\ \\ = > x ^{3} + \frac{1}{x ^{3} } + 3 \sqrt{3} = 3 \sqrt{3} \\ \\ = > x ^{3} + \frac{1}{x ^{3} } = 3 \sqrt{3} - 3 \sqrt{3} \\ \\ = > x ^{3} + \frac{1}{x ^{3} } = 0$

FINAL ANSWER...

$= > x ^{3} + \frac{1}{x ^{3} } = 0$