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The value of sqrt(7+sqrt(7-sqrt(7+sqrt(7...

The value of `sqrt(7+sqrt(7-sqrt(7+sqrt(7-….))))` upto `oo` is

A

5

B

4

C

3

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Let `x=sqrt(7+sqrt(7-sqrt(7+sqrt(7-…..oo))))`
`impliesx=sqrt(7+sqrt(7-x))` [on squaring both sides]
`impliesx^(2)-7=sqrt(7-x)`
`impliesx^(4)-14x^(2)+x+42=0`
`implies(x-3)(x^(3)+3x^(2)-5x-14)=0`
`implies(x-3)(x+2)(x^(2)+x-7)=0`
`impliesx-3,-2,(-1+-sqrt(29))/2`
`:.x=3 [ :' xgtsqrt(7)]`
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