Question

How do you find all real solutions to the following equation: `(x^2-7x+11)^(x^2-2x-35)=1`?

Answer 1

`x={-5,7}`

Explanation:

We know that `a^0=1` so making `x^2-2x-35=0` the solutions are `x={-5,7}` but we know also that `a` must be non null. Solving now

`x^2 - 7 x + 11 =0` we have `x = 1/2 (7 pm sqrt[5]) ne {-5,7}`

Finally the equation is meaningful for

`x={-5,7}`