First slide

Arithmetic progression

Question

The value of x for which $\frac{1}{1 + \sqrt{x}}, \frac{1}{1 - x}, \frac{1}{1 - \sqrt{x}}$ are in A.P lie in

Moderate

A

$(- 1, 1)$
B

$[0, 1) \cup (1, \infty)$
C

$(0, \infty)$
D

$(- 2, 2)$

Solution

For $\sqrt{x}$ to be defined we must have $x \geq 0$ .
Also for $\frac{1}{1 - x} a n d \frac{1}{1 - \sqrt{x}}$ to be defined we must have $x \neq 1.$
$F o r x \in [0, 1) \cup (1, \infty)$ , We have $\frac{2}{1 - x} = \frac{1}{1 - \sqrt{x}} + \frac{1}{1 + \sqrt{x}}$

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