MCQ
The value of $x = \sqrt {2 + \sqrt {2 + \sqrt {2 + .....} } } $is
- A$-1$
- B$1$
- ✓$2$
- D$3$
✓
Answer
Correct option: C.
$2$
c
(c) $x = \sqrt {2 + x} $$⇒$ ${x^2} - x - 2 = 0$
(c) $x = \sqrt {2 + x} $$⇒$ ${x^2} - x - 2 = 0$
$⇒$ $(x - 2)(x + 1) = 0$ $⇒$ $x = 2, - 1$
But $\sqrt {2 + \sqrt {2 + .....} } \ne - 1$, so it is equal to $2.$
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