+0  
 
0
273
5
avatar+31 

Determine the sum of all real numbers satisfying:

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

 Feb 18, 2022
 #1
avatar+117852 
+1

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

 Feb 18, 2022
 #2
avatar+31 
0

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

asiandude  Feb 19, 2022
 #3
avatar+117852 
+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

 Feb 19, 2022
edited by Melody  Feb 19, 2022
 #4
avatar+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
avatar+117852 
+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

8 Online Users

avatar