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4-2.Quadratic Equations and Inequations
medium
The number of solutions of $\frac{{\log 5 + \log ({x^2} + 1)}}{{\log (x - 2)}} = 2$ is
A
$2$
B
$3$
C
$1$
D
None of these
Solution
(d) We have $\frac{{\log 5 + \log ({x^2} + 1)}}{{\log (x – 2)}} = 2$
==> $\log \{ 5({x^2} + 1)\} = \log {(x – 2)^2} \Rightarrow 5({x^2} + 1) = {(x – 2)^2}$
$ \Rightarrow $ $4{x^2} + 4x + 1 = 0 \Rightarrow x = – \frac{1}{2}$
But for $x = – \frac{1}{2}\log (x – 2)$ is not meaningful.
Hence it has no root.
Standard 11
Mathematics
