If x = 6 + 6 + 6 + .... to , , , then - Vidyadip

MCQ

If $x = \sqrt {6 + \sqrt {6 + \sqrt {6 + ....{\rm{to}}\,\,\infty } } ,} $ then

A
$x$ is an irrational number
B
$2 < x < 3$
✓
$x = 3$
D
None of these

✓

Answer

Correct option: C.

$x = 3$

c
(c) $x = \sqrt {6 + x} $, $x > 0\,\, \Rightarrow {x^2} = 6 + x,x > 0$

$ \Rightarrow {x^2} - x - 6 = 0,\,x > 0$ $ \Rightarrow x = 3,x > 0$.

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