Question

if `(log)_y x+(log)_x y=2,x^2+y=12 ,` the value of `x y` is 9 (b) 12 (c) 15 (d) 30

Answer 1

Let `log_y^x=t`
`t+1/t=2`
`t^2+1=2t`
`t^2-2t+1=0`
`(t-1)^2=0`
`t=1`
`log_y^x=1`
`x=y`
`x^2+x=12`
`x^2+x-12=0`
`x^2+4x-3x-12=0`
`x(x+4)-3(x+4)=0`
`(x+4)(x-3)=0`
`x=3,-4`
x can not be negative
so, x=y=3
Option A is correct.