Question

The sum of all the real values of $x$ satisfying the equation ${2019}^{(x-1)(x^2+5x-50)}=1$ is :

• A. $16$
• B. $14$
• C. $-4$
• D. $-5$

Answer 1

The correct option is C $-4$

${2019}^{(x-1)(x^2+5x-50)}=1$

$\Rightarrow {2019}^{(x-1)(x^2+5x-50)}={2019}^o[\because a^o=1]$

$\Rightarrow (x-1)(x^2+5x-50)=0$

$\Rightarrow (x-1)(x-5)(x+10)=0$

$\Rightarrow x=-10,5,1$

$\therefore$ sum $=-10+5+1$

$=-4$