First slide

Theory of expressions

Question

Value of
$x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots up t o \infty}}}$
is

Moderate

A

3
B

2
C

1
D

none of these

Solution

We can write (1) as
$\begin{array}{l} x = \sqrt{6 + x} \Rightarrow x^{2} = 6 + x \\ \Rightarrow x^{2} - x - 6 = 0 \Rightarrow (x - 3) (x + 2) = 0 \\ \Rightarrow x = 3, - 2 \end{array}$
$As x > 0, we take x = 3$

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