Question

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

• A. 6
• B. 5
• C. 3
• D. -4

Answer 1

The correct option is C 3

given equation:

$(x²-5x+5{)}^{(x²+4x-60)}=1$

we know that any integer or expression when have power $0$ is equal to $1$

so,

$(x²+4x-60)=0$

by using quadratic factorisation

$(x-6)(x+10)=0$

$x=6,x=-10$

Now,

$x^2-5x+5=1$

$x^2-5x+4=0$

$(x-4)(x-1)=0$

$x=4,x=1$

$x=-10,1,2,4,6$

Sum of values of $x=-10+1+2+4+6$

$=3$

so sum of all real values of $x$ satisfying the equation $=3$