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if (log)y x+(log)x y=2,x^2+y=12 , the va...

if `(log)_y x+(log)_x y=2,x^2+y=12 ,` the value of `x y` is

A

9

B

12

C

15

D

30

Text Solution

Verified by Experts

Let `logx/(b-c) = logy/(c-a) = logz/(a-b) = k`
`=>logx = kb-kc,logy = kc-ka,logz = ka-kb`
`=>logx+logy+logz = kb-kc+kc-ka+ ka-kb`
`=>log(xyz) = 0`
`=>log(xyz) = log1`
`=>xyz = 1`
So, option `(a)` is the correct option.
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