The value of `6+(log)_(3/2)[1/(3sqrt(2)) * sqrt{ (4 - 1/(3sqrt(2))) sqrt(4 - 1/(3sqrt(2))....... }` is ...............

Options

A. `3sqrt(2)`
B. `sqrt(2)`
C. `4`
D. `6`

Answer

C

Explanation

`y=sqrt((4-1/(3sqrt2))sqrt((4-1/(3sqrt2)sqrt((4-1/(3sqrt2)...`

`y=sqrt(4-1/(3sqrt2)y`

`y^2=4-y/(3sqrt2)`

`3sqrt2y^2+y-12sqrt2=0`

`y=(-1+sqrt(1-(-12sqrt2)*(3sqrt2)*4))/(2*3sqrt2)`

`y=(-1+sqrt(1+144*2))/(2*3sqrt2)`

`y=(-1+sqrt289)/(6sqrt2)`

`y=8/(3sqrt2)`

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