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Question

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


A
5
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B
16
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C
14
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D
4
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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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