If x^2 + 125x^2 = 8/5 and x > 0, then what is the value of x^3 + 1125x^3 = ?

Answer: Option C

$$\begin{array}{rl}& \because x^2+\frac{1}{25x^2}=\frac{8}{5}\\ & \Rightarrow x^2+\frac{1}{25x^2}+2x\times \frac{1}{5x}=\frac{8}{5}+\frac{2}{5}\\ & \Rightarrow {\left(x+\frac{1}{5x}\right)}^2=2\\ & \Rightarrow x+\frac{1}{5x}=\sqrt{2}\\ & \text{On cubing both sides}\\ & \Rightarrow x^3+\frac{1}{125x^3}+3\times \frac{1}{5}\left(\sqrt{2}\right)={\left(\sqrt{2}\right)}^3\\ & \Rightarrow x^3+\frac{1}{125x^3}=2\sqrt{2}-\frac{3\sqrt{2}}{5}\\ & \Rightarrow x^3+\frac{1}{125x^3}=\frac{7\sqrt{2}}{5}\end{array}$$