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Question
If `2^(x + y) = 2^(x - y) = sqrt(8)` then the value of y is ______.
Options
`1/2`
`3/2`
0
none of these
MCQ
Fill in the Blanks
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Solution
If `2^(x + y) = 2^(x - y) = sqrt(8)` then the value of y is 0.
Explanation:
`sqrt(8) = 2^(3/2)`, so `2^(x + y) = 2^(3/2)` and `2^(x - y) = 2^(3/2)`.
Thus, `x + y = 3/2` and `x - y = 3/2`.
Subtract the second from the first:
2y = 0
⇒ y = 0
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