If x^2 + 1x^2 = 319 and x > 0, then what is the value of x^3 + 1x^3 = ?

Answer: Option B

$$\begin{array}{rl}& x^2+\frac{1}{x^2}=\frac{31}{9}\\ & x+\frac{1}{x}=\sqrt{\frac{31}{9}+2}\\ & x+\frac{1}{x}=\frac{7}{3}\\ & x^3+\frac{1}{x^3}=n^3-3n\\ & x^3+\frac{1}{x^3}={\left(\frac{7}{3}\right)}^3-3\times \frac{7}{3}\\ & x^3+\frac{1}{x^3}=\frac{343}{27}-7\\ & x^3+\frac{1}{x^3}=\frac{343-7\times 27}{27}\\ & x^3+\frac{1}{x^3}=\frac{154}{27}\end{array}$$