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Exponent Problem

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Exponent Problem

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If x is an integer, is 16^x + 16^-x = b
(1) 4^x + 4^-x = √(b+2)
(2) x>0

I know that the answer is A. But my question is, why, when you square on both sides doesn't √(b+2) end up being |b+2|?

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Senior | Next Rank: 100 Posts Default Avatar
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That is because the min value of 4^x+4^-x is 2, at x=0. As a result, the smallest value of b is 0 and there is no need for the absolute value. Based on the constraints, the value of sqrt(b+2) cannot be negative for any integer x.

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Junior | Next Rank: 30 Posts Default Avatar
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Yes ideally on squaring, the absolute value is considered and here the value of b is unknown. But you may note that whatever the value of x be the left hand side of the equation that is 16^x + 16^-x will always be positive. You can check for yourself by taking examples, by keeping different values for x, you will find that the answer is always positive.

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