$\sqrt{x^3}$ - 1/ $\sqrt{x^3}$ =14 find x+1/x
You asked:
Given \(\sqrt{{x}^{3}} - \frac{1}{\sqrt{{x}^{3}}} = 14\) evaluate the expression \(x + \frac{1}{x}\).
MathBot Answer:
\[x + \frac{1}{x} = \frac{1}{2 \sqrt{2} + 3} + 2 \sqrt{2} + 3\]
The solution is: \[x = 3 + 2 \sqrt{2} \approx 5.8284271\]
By substituting this value into the expression, we find that: $$\begin{aligned}x + \frac{1}{x} &= \frac{1}{2 \sqrt{2} + 3} + \left(2 \sqrt{2} + 3\right)\\&= \frac{1}{2 \sqrt{2} + 3} + 2 \sqrt{2} + 3\end{aligned}$$