Question

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

Answer 1

Correct Answer - 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`