### Find all real solutions of $\left(x^2-7x+11\right)^{\left(x^2-11x+30\right)}=1$

8
views
0
13 days ago by
$\left(x^2-7x+11\right)^{\left(x^2-11x+30\right)}=1$

First thing I noticed was the exponent can be factorised $x^2-11x+30=(x-5)(x-6)$

But I don't know what to do from here
Community: Everyday Math

2
13 days ago by
Remember that any number (except 0) to the power of 0 is 1.

Which means if  $x^2-11x+30=0$  $\left(x^2-7x+11\right)^{\left(x^2-11+30\right)}=1$

Also remember that 1 to the power of any number is 1.

So the second case will be:  $x^2-7x+11=1$

And there is one more case, -1 to the power of even number is 1.

So the final case will be  $x^2-7x+11=-1$, where $x^2-11x+30$ is even