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.The value of sqrt(8+2sqrt(8+2sqrt(8+2s...

.The value of `sqrt(8+2sqrt(8+2sqrt(8+2sqrt(8+2sqrt(8+...oo)))))` is equal to

A

10

B

8

C

6

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Let `y=sqrt(8+2y)`
`rArr y^(2) = 8+2y rArry^(2) - 2 y - 8 =0`
`rArr ( y+2) (y-4) = 0`
`rArr y=4,-2`
Hence, required value of given expression is 4.
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