Determine the sum of all real numbers \(x\) satisfying \((x^2-4x+2)^{x^2-5x+2} = 1.\)

Guest May 20, 2022

#1**+3 **

Case 1: x²-5x+2 = 0

The roots are both real. The sum of the roots is equal to -b/a, which is 5 here.

Case 2: x²-4x+2=1

x²-4x+1=0

The roots are both real. The sum of the roots is equal to -b/a, which is 4 here.

Case 3: x²-4x+2=-1

x²-4x+3=0

The roots are both real. The sum of the roots is equal to -b/a, which is 4 here.

5+4+4 = 13

WhyamIdoingthis May 20, 2022

#3**+1 **

Why has just made a careless mistake and it you were interested in more than just plugging a numberinto a box you would easily have found it.

Hence you are just here to cheat.

Please whyamIdoingthis, do not change your answer, you logic is good and it is good to out cheaters.

In my view your answer is better than if you had not made this trivial error.

Melody
May 22, 2022