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4-2.Quadratic Equations and Inequations
hard
Let $y = \sqrt {\frac{{(x + 1)(x - 3)}}{{(x - 2)}}} $, then all real values of $x$ for which $y$ takes real values, are
A
$ - 1 \le x < 2$ or $x \ge 3$
B
$ - 1 \le x < 3$ or $x > 2$
C
$1 \le x < 2$ or $x \ge 3$
D
None
(IIT-1980)
Solution
(a) $y = \sqrt {\frac{{(x + 1)(x – 3)}}{{(x – 2)}}} $
Here $x$ cannot be $2$.
==> Either both ${N^r}$ and ${D^r}$ are positive
$x \ge – 1,x \ge 3$ and $x > 2 \Rightarrow x \ge 3$…..$(i)$
Or ${N^r}$ is negative and ${D^r}$ is negative
$x \ge – 1$ and $x < 2 \Rightarrow – 1 \le x < 2$…..$(ii)$
From $(i)$ and $(ii),$ $ – 1 \le x < 2$ or $x \ge 3$.
Standard 11
Mathematics
