Question

The number of real solutions of the equation [9/x]^x=-3+x-x^2 is?

Answer 1

No real Solutions.

Explanation:

For `x>0` is `(9/x)^x>0` (for `x<0` is `(9/x)^x` not defined, `x` as a real number)

and for `x>0` is

`-3+x-x^2<0`
multiplying by `-1`

`x^2-x+3>0`
and this is

`x^2-2*(1/2)*x+1/4+3-1/4>0`

`(x-1/2)^2+11/4>0` which is true for all `x` with `x>0`