पद `6+log_(3/2)(1/(3sqrt(2))sqrt(4-1/(3sqrt(2))sqrt(4-1/(3sqrt(2))sqrt(4-1/(3sqrt(2))…………..))))` का मान है

Answer

4

Explanation

यहां माना `(1/(3sqrt(2))sqrt(4-1/(3sqrt(2))sqrt(4-1/(3sqrt(2))sqrt(4-1/(3sqrt(2))…………..))))`

`x = 1/(3sqrt(2)) * sqrt(4 - x)`

` 2sqrt(2) * x = sqrt(4 - x)`

`18x ^ 2 = 4 - x`

`18x ^ 2 + x - 4 = 0`

`x = (- 1 pm sqrt(1 + 4* 18*4))/36`

`= (-1 pm sqrt (1+288))/ 36`

` 1(-1 pm 17)/ 36`

`x = (- 1 - 17)/36, " "( - 1 + 17)/36`

`x = - 18/36, x = 16/36`

` x = - 1/2 ,`[असंभव `xgt0`]

` x = 4/9`

अब `6+log_(3/2)4/9`

`=6+log_(3/2) ( 2/ 3 )^ 2`

`=6+2log_(3/2) ( 2/ 3 )`

`=6+2log_(3/2) ( 3/ 2 )^(-1)`
`=6-2log_(3/2) ( 3/ 2 )`
`=6-2=4`