Evaluate √(3+√(3+√(3…)) )?

√{3 + √[3 + (√3 + √3 ...)]}

Let x = √{3 + √[3 + (√3 + √3 ...)]}
√{3 + √[3 + (√3 + √3 ...)]} = √(3 + x)
x = √(3 + x)
x^2 = 3 + x
x^2 - x - 3 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -1
c = -3

x = [1 ±√(1 + 12)]/2
x = [1 ±√13]/2

∴ x = [1 ±√13]/2

Let the expression be x so Rt(x+3) = x or x^2 = x+3
Now solve x^2 - x - 3 = 0 and take the root tht is +ve.

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