Seemingly Easy??

[bandofhorses11]

Hi, I've been trying to solve this problem algebraically for a while, but I can't seem to figure it out. How would you solve this step by step? Thanks:

x^3 + x = 40

 

[daon]

It will have one positive real root (a cubic whos derivative is always positive). The fact that the root is positive is that the function f(x)=x^3+x-40 is <0 when x<0 and it is always increasing.

A quick check tells you there is no rational roots. So unless you happen to know the root, you might need to use calculus to approximate it or get the exact answer with something a little fancier (akin to the "quadratic formula for polynomials of degree 2): http://en.wikipedia.org/wiki/Cubic_function

This a LONG and TEDIUS method.