SOLUTION: If y = log2( x + sqrt(x^+1) ), then 2^y - 2^-y = _______ x

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Question 1037480: If y = log2( x + sqrt(x^+1) ), then 2^y - 2^-y = _______ x
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+log%282%2C+%28x+%2B+sqrt%28x%5E2%2B1%29%29+%29 ==> 2%5Ey+=+x+%2B+sqrt%28x%5E2%2B1%29+.
Also, 2%5E%28-y%29+=+1%2F%28x+%2B+sqrt%28x%5E2%2B1%29%29+.
==> 2%5Ey+-+2%5E%28-y%29+=+x+%2B+sqrt%28x%5E2%2B1%29+-++1%2F%28x+%2B+sqrt%28x%5E2%2B1%29%29
= %28x%5E2+%2B+2x%2Asqrt%28x%5E2%2B1%29+%2B+x%5E2%2B1+-1%29%2F%28x+%2B+sqrt%28x%5E2%2B1%29%29
= .
The answer is now obvious.