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The Brainliest Answer!
2015-02-18T13:56:21+05:30
Let x =  \sqrt{6+ \sqrt{6+ \sqrt{6+ \sqrt{6+ \sqrt{6+.........} } } } }

Squaring on both sides

x^2 = 6 + \sqrt{6+ \sqrt{6+ \sqrt{6+ \sqrt{6+ \sqrt{6+.........} } } } }

x^2 = 6 + x

x^2 - x - 6 = 0

Solving the quadratic equation, we get

(x-3)(x+2) = 0

x = 3

2 5 2