SOLUTION: 3^2x + 3^-2x = 14 3^x + 3^-x = ?

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Question 1020933: 3^2x + 3^-2x = 14
3^x + 3^-x = ?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is 4.
To see why,
3%5E%282x%29%2B3%5E%28-2x%29+=+14 <==> 3%5E%282x%29%2B1%2F3%5E%282x%29+=+14
<==> 3%5E%284x%29+%2B+1+=+14%2A3%5E%282x%29
<==> 3%5E%284x%29+-+14%2A3%5E%282x%29%2B1+=+0
By the quadratic formula, we then get
3%5E%282x%29+=+%2814%2B-sqrt%28192%29%29%2F2
<==>3%5E%282x%29+=+7%2B-sqrt%2848%29 ==> 3%5Ex+=+sqrt%287%2B-sqrt%2848%29%29
(Note that these two values are inverses of each other, so that 3%5Ex%2B3%5E%28-x%29 will have only one value, regardless whether we choose 3%5Ex+=+sqrt%287%2Bsqrt%2848%29%29 or 3%5Ex+=+sqrt%287-sqrt%2848%29%29.)
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