+0

# help

0
96
5
+31

Determine the sum of all real numbers satisfying:

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

Feb 18, 2022

#1
+117434
+1

There is nothing to satisfy.  You are most likely missing an equal sign ...

Feb 18, 2022
#2
+31
0

sorry, it's $$(x^2-4x+2)^{x^2-5x+2}=1$$

asiandude  Feb 19, 2022
#3
+117434
+1

This will happen when

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

Feb 19, 2022
edited by Melody  Feb 19, 2022
#4
+31
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
+117434
+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

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