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  • The sum of all real values of x satisfying the equation <img alt="( x^{2} -5x+5 )^{x^{2}+4x-60}=1" src="/latex-image/?%28%20x%5E%7B2%7D%20-5x&plus;5%20%29%5E%7Bx%5E%7B2%7D&plus;4x-60%7

The sum of all real values of x satisfying the equation ( x^{2} -5x+5 )^{x^{2}+4x-60}=1 is

 

Option: 1

3


Option: 2

-4


Option: 3

6


Option: 4

5


Answers (1)

best_answer

 \\(x^2 -5x +5 )^{x^2+4x-60}= 1 \\\\ \Rightarrow x^2 -5x +5 = 1 \: \: or \: \: x^2+4x-60=0

\Rightarrow x^2 -5x +4 = 0 \: \: or \: \: x^2+4x-60=0

\Rightarrow (x-4)(x-1)= 0 \: \: or \: \: (x+10)(x-6)= 0

x= 4, 1 \: \: or \: \: x = 6, -10

Also there is a case 

x^2 -5x +5 = -1 \: \: \: \& \: \: \: x^2+4x-60=even \: \: no.

x^2 -5x +6 = 0 \implies (x-2)(x-3)=0 \implies x=2,3

For\,\,x=2\,\,,x^2 +4x -60 = -48 (accepted \,\,as\,\,it\,\,is\,\,even)

For\,\,x=3\,\,,x^2 +4x -60 = -39 (not \, \, \, accepted \,\,as\,\,it\,\,is\,\,not\,\,even)

 

So solutions are 4,1,6,-10,2

Sum = 4+1+6+(-10)+2= 3 

 

 

 

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