Question

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

A
5
B
16
C
14
D
4

Solution

## The correct option is C $$-4$$For $$\displaystyle 2^{\displaystyle (x-1)(x^2+5x-50)}=1$$$$\displaystyle (x-1)(x^2+5x-50)=0$$$$\therefore \displaystyle x-1=0$$ or $$\displaystyle x^2+5x-50=0$$If $$\displaystyle x-1=0\Rightarrow x=1$$If $$\displaystyle x^2+5x-50=0$$, then$$\displaystyle x^2+10x-5x-50=0$$$$\displaystyle x(x+10)-5(x+10)=0$$$$\displaystyle (x+10)(x-5)=0$$$$\displaystyle x=-10, 5$$Real values of $$x=-10,1,5$$sum of the real values of x$$=-10+5+1=-4$$.Mathematics

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