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Question

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


A
16
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B
14
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C
4
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D
5
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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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