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

 Aug 4, 2021
 #1
avatar+34316 
+1

Note that anything raised to the '0' power = 1

   5^0 =  1      123^0 = 1

so the exponent = 0

x^2 -5x + 2 = 0

 

 

Quadratic Formula shows x = 1/2 ( 5 +-sqrt(17) )        sum = 5

 Aug 4, 2021
 #2
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+1

you forgot the possibility that x^2-4x+2=+-1

Guest Aug 4, 2021
 #3
avatar+34316 
0

Correct......   what do YOU find for that answer?    I'll let you answer that......  Thanx !    ~EP

ElectricPavlov  Aug 4, 2021

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