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

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-4

answer is C.

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Detailed Solution

${(x^{2} - 5 x + 5)}^{x^{2} + 4 x - 60} = 1$

Case-I: $x^{2} - 5 x + 5 = 1$

x=1,4

Case-II: $x^{2} - 5 x + 5 = - 1$

And $x^{2} + 4 x - 60$ even number

x=2,3 and 3 is not possible

Case –III: $x^{2} - 5 x + 5$ is any real number

$x^{2} + 4 x - 60 = 0$

X= -10,6

sum of the solutions

$x = - 10 + 6 + 2 + 1 + 4 = 3$

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