SOLUTION: find the sum of all of the real values of x satisfying the following equation (x^2 - 5x + 5)^x^2 - 17x + 70 = 1 a 5 b 10 c 17 d 22 e 27

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: find the sum of all of the real values of x satisfying the following equation (x^2 - 5x + 5)^x^2 - 17x + 70 = 1 a 5 b 10 c 17 d 22 e 27      Log On


   

Question 252528: find the sum of all of the real values of x satisfying the following equation
(x^2 - 5x + 5)^x^2 - 17x + 70 = 1
a 5 b 10 c 17 d 22 e 27
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the roots of this quadratic looking equation is -b/a. So, we get
17 / (X^2 - 5X + 5). The denominator cannot = 0. So we factor the denominator as
X = (5 +- sqrt(5))/2
There are 2 roots here and if we add them, we get 5.
So, it appears that the answer will be 5 [A].
Hope that helps.