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

Solution

## The correct option is C $$-4$$$$2019^{(x-1)(x^2+5x-50)}=1$$$$\Rightarrow 2019^{(x-1)(x^2+5x-50)}=2019^o\quad [\because a^o=1]$$$$\Rightarrow (x-1)(x^2+5x-50)=0$$$$\Rightarrow (x-1)(x-5)(x+10)=0$$$$\Rightarrow x=-10, 5, 1$$$$\therefore$$ sum $$=-10+5+1$$            $$=-4$$Mathematics

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