Question
$$\frac{1+x}{2}+\frac{3-x}{4} = x(x^3-2x)^2$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1+x}{2}+\frac{3-x}{4} &= x(x^3-2x)^2&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1+x}{2}+4\frac{3-x}{4} &= 4x(x^3-2x)^2&& \text{cancel out the denominators} \\[1 em]2x+2+3-x &= 4x(x^3-2x)^2&& \text{simplify left and right hand side} \\[1 em]x+5 &= 4x(x^6-4x^4+4x^2)&& \\[1 em]x+5 &= 4x^7-16x^5+16x^3&& \text{move all terms to the left hand side } \\[1 em]x+5-4x^7+16x^5-16x^3 &= 0&& \text{simplify left side} \\[1 em]-4x^7+16x^5-16x^3+x+5 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Equations Solver