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

Options

A. -4
B. 6
C. 5
D. 3

Answer

4

Explanation

`(x^(2) - 5x + 5 )^(x^(2 + 4x - 60)) = 1 `
Case I:
` x^(2) + 4x - 60 = 0` ltbRgt ` therefore (x - 6) (x + 10) = 0`
` therefore x = 6 , - 10 `
Case II :
` x^(2) - 5x + 5 = 1`
`therefore x^(2) - 5x + 4 = 0 `
`therefore (x - 1) (x - 4) = 0 `
`therefore x = 1, 4`
Case III :
` x^(2) - 5x + 5 = - 1 and x^(2) - 4x - 60 ` is even number
` therefore x^(2) - 5 x + 6 = 0 `
` therefore (x - 2) (x - 3) = 0 `
` therefore x = 2, 3 `
But for x = 3 , `x^(2) - 4x - 60 ` is odd.
Hence x = 2 only.
Thus solution are 6, - 10, 1,4,2
Sum of solution is 3