Practicing Success
If $\frac{4}{3}(x^2+\frac{1}{x^2}) = 110 \frac{2}{3}$, find $\frac{1}{9}(x^3-\frac{1}{x^3})$, where x > 0. |
84 85 74 76 |
84 |
If $\frac{4}{3}(x^2+\frac{1}{x^2}) = 110 \frac{2}{3}$, find $\frac{1}{9}(x^3-\frac{1}{x^3})$ = $(x^2+\frac{1}{x^2})$ = \(\frac{332}{3}\) × \(\frac{3}{4}\) = $(x^2+\frac{1}{x^2})$ = 83 = x - \(\frac{1}{x}\) = \(\sqrt {83-2}\) = 9 Now, x3 - \(\frac{1}{x^3}\) = 93 + 3 × 9 = 756 $\frac{1}{9}(x^3-\frac{1}{x^3})$ = $\frac{1}{9}(756)$ = 84 |