if-9x-2-1-x-2-3-then-27x-3-1-x-3-

Question Number 161169 by MathsFan last updated on 13/Dec/21

i f 9 x^{2} + \frac{1}{x^{2}} = 3

t h e n

27 x^{3} + \frac{1}{x^{3}} = ?

Answered by Rasheed.Sindhi last updated on 13/Dec/21

9 x^{2} + \frac{1}{x^{2}} = 3; 27 x^{3} + \frac{1}{x^{3}} = ?

{(3 x + \frac{1}{x})}^{2} = 9 x^{2} + 6 + \frac{1}{x^{2}} = 3 + 6 = 9

3 x + \frac{1}{x} = \pm 3

{(3 x + \frac{1}{x})}^{3} = {(\pm 3)}^{3}

27 x^{3} + \frac{1}{x^{3}} + 3 (3 x) (\frac{1}{x}) (3 x + \frac{1}{x}) = \pm 27

27 x^{3} + \frac{1}{x^{3}} + 9 (\pm 3) = \pm 27

27 x^{3} + \frac{1}{x^{3}} \pm 27 = \pm 27

27 x^{3} + \frac{1}{x^{3}} = \pm 27 \mp 27 = 0

Answered by Rasheed.Sindhi last updated on 15/Dec/21

27 x^{3} + \frac{1}{x^{3}} = (3 x + \frac{1}{x}) (9 x^{2} - 3 + \frac{1}{x^{2}})

= (3 x + \frac{1}{x}) (3 - 3)

= (3 x + \frac{1}{x}) (0) = 0

USED FORMULA :

\begin{matrix} a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2}) \end{matrix}

Commented by MathsFan last updated on 13/Dec/21

t h a n k y o u s i r .