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\sqrt 6 %2B \sqrt 6 %2B \sqrt 6 %2B

Answer»

Let us assume : x= root(6+root(6 + root(6 + ………

So,

x= root(6+x)

x^2=6+x

x^2-x-6=0

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

So, x=3 or -2.

But taking -2 as the answer would mean we are taking root of (-2) . Considering the fact that x belongs to the set of real numbers , we discard the solution x=-2.

So the answer is x =3.

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