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Evaluate x=sqrt(6+sqrt(6+sqrt(6+.....ood...

Evaluate `x=sqrt(6+sqrt(6+sqrt(6+.....oodot)))`

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Verified by Experts

Let `x = sqrt(6+sqrt(6+_sqrt(6+...infty.)))`. Then
`xsqrt(6+x)`
or `x^(2) = 6 + x`
or `x^(2) - x - 6 = 0 `
or `(x-3)(x +2) = 0`
or x = 3, -2
But, the given expression is positive. So, x = 3 . Hence, the value of the given expression is 3
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