Question

$\sqrt{6 + \sqrt{6 + \sqrt{6 + ...........} } }$
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Answer 1

Answer:

Hi there!

Given : x = √6 + √6 + √6 +... ---(i)

Then,

x = √6 + x --- From Eqn. (i)

On squaring both sides,

⇒ x² = 6 + x

⇒ x² - x - 6 = 0

⇒ x² - 3x + 2x - 6 = 0

⇒ x(x-3) + 2(x-3) = 0

⇒ x = 3 Or x = -2

But x is a natural number.

∴ x = 3

Answer 2

Answer:

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Step-by-step explanation:

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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