Question

Solve ((x+5)^5) + ((x-1)^5) >= 244 ?

Answer 1

`x ge -1.7045...`

Explanation:

`f(x) = (x+5)^5 + (x-1)^5 -244`

`f` necessarily has at least one real zero, being of odd degree.

`f'(x)=5(x+5)^4 + 5(x-1)^4`

We note the derivative is always positive, so `f` is monotonically increasing. So the solution to our inequality is

`x ge r`

where `r` is the sole real zero of `f`.

There's almost certainly no closed form for `r`; Alpha gives a numerical zero `r approx -1.7045.`

`x ge -1.7045...`