Question

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

• A. 3
• B. -4
• C. 6
• D. 5

Answer 1

Answer: (A)

${\left(x^2-5x+5\right)}^{x^2+4x-60}=1={\left(x^2-5x+5\right)}^0$
$\Rightarrow x^2+4x-60=0\left[a^x=a^y\Rightarrow x=yifa\ne 1,0,-1\right]$
$x=-10,6$
& base $x^2-5x+5=0$ or $1$ or $-1$
If $x^2-5x+5=0$

But it will not satisfy original equation .
Hence solutions are - $10,6,4,1,2$
So, sum of solutions $=-10+6+4+1+2=3$