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If log(y) x + log(x) y = 2, x^(2)+y = 12...

If `log_(y) x + log_(x) y = 2, x^(2)+y = 12` , then the value of xy is

A

9

B

12

C

15

D

21

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` t=log_(y) x(x, y gt 0, and ne 1)," then " t+1/t = 2 or (t-1)^(2) = 0`
` :. T = log_(y) x = 1 , i.e., x = y `.We get
` x^(2) + x - 12 = 0 x = -4, 3`.
x = 3 only (-4 rejected)
` :. Y = 3`,
` :. X = 9`
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