Question
$$320 = x^2+\frac{64}{x^2}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 320 &= x^2+\frac{64}{x^2}&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\cdot320 &= x^2x^2+x^2\cdot\frac{64}{x^2}&& \text{cancel out the denominators} \\[1 em]320x^2 &= x^4+64&& \text{move all terms to the left hand side } \\[1 em]320x^2-x^4-64 &= 0&& \text{simplify left side} \\[1 em]-x^4+320x^2-64 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver