The value of x = 2 + 2 + 2 + ..... is - Vidyadip

Question

The value of $x = \sqrt {2 + \sqrt {2 + \sqrt {2 + .....} } } $is

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Answer

c
(c) $x = \sqrt {2 + x} $$⇒$ ${x^2} - x - 2 = 0$

$⇒$ $(x - 2)(x + 1) = 0$ $⇒$ $x = 2, - 1$

But $\sqrt {2 + \sqrt {2 + .....} } \ne - 1$, so it is equal to $2.$

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