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