Determine the sum of all real numbers satisfying:

\((x^2-4x+2)^{x^2-5x+2}\)

asiandude Feb 18, 2022

#3**+1 **

This will happen when

x^2-5x+2 = 0 ( so long as x^2-4x+2 isn't 0 as well. )

use the quadratic formula

Melody Feb 19, 2022

#4**0 **

Ok, the sum will equal 9 in that case. But I think there are other cases too, for example when x^2-4x+2 = 1. Can you help me think of other ones?

asiandude
Feb 20, 2022

#5**+1 **

\(x^2-5x+2 = 0\\ x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x = {5 \pm \sqrt{25-8} \over 2}\\ \)

**The sum of these is 5**

Just checking that those answsers are valid. what can x not be

\(x^2-4x+2\ne0\\ x \ne {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x \ne {4 \pm \sqrt{16-8} \over 2}\\\)

Yes the answer is fine.

Melody
Feb 20, 2022