Algebraic equation problem - finding $x$
$$(x^2 +100)^2 =(x^3 -100)^3$$
How to solve it?
Solution 1:
hint Define $f(x)=(x^2+100)^\frac{1}{3}$, notice that for $x\geq 0$
is increasing.
Compute its inverse function $$f^{-1}(x)=(x^3-100)^\frac{1}{2}$$
Where can $f$ and $f^{-1}$ intersect? Remember that the graph of $f^{-1}$ is the reflection of the graph of $f$ across the line $y=x$
Solution 2:
This is "cheating", of course:
