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

Options

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

Answer

C

Explanation

`(x^(2)-5x+5)^(x^(2)+4x-60)=1`
Case I
`x^(2)-5x+5=1` and `x^(2)+4x-60` can be any real number
`impliesx=1,4`
Case II
`x^(2)-5x+c=-1` and `x^(2)+4x-60` has to be an even number ltbr gt`impliesx=2,3`
For `x=2,3`
For `x=3, x^(2)+4x-60` is odd `:.!=3`
Hence `x=2`
Case III `x^(2)-5x+5` can be any real number and
`x^(2)+4x-60=0`
`impliesx=-10,6`
`implies` Sum of all values o `x=1+4+2-10+6=3`