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# What is sum of all solutions to equation: x^(x^2 + 2)

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Re: What is sum of all solutions to equation: x^(x^2 + 2) [#permalink]
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Re: What is sum of all solutions to equation: x^(x^2 + 2) [#permalink]
this is my versione
we have x^2+2 =4x+14
=x^2-4x-12=0 solution -> (x-6)(x+2)

roots are -6, +2= -4
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Re: What is sum of all solutions to equation: x^(x^2 + 2) [#permalink]
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BrentGMATPrepNow -

Case 1: Equation will be equal if the powers are equal given the base is same. This gives us -2 & 6 as values of the indices of x.
Case 2: The base i.e. x will always be equal to x if it is 1 even if it is raised to any power.

Thus solution will be a combination of both Case I & Case II i.e. -2+6+1=5.

Hence, C.
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Re: What is sum of all solutions to equation: x^(x^2 + 2) [#permalink]
@@BrentGMATPrepNow I didn't get it. How x=0/1 works here. After putting the values we didn't get the same ans on both sides

Posted from my mobile device
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Re: What is sum of all solutions to equation: x^(x^2 + 2) [#permalink]