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4-2.Quadratic Equations and Inequations
hard
The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by
A
$ \pm 1/9,\; \pm 2$
B
$ - 1/9,\;2$
C
$1/9,\; - 2$
D
$ - 1/9,\; - 2$
Solution
(d) Domain of definition of the function $y = \sqrt {x(x – 3)} $ is $x(x – 3) \ge 0$ i.e. $x \le 0$ or $x \ge 3$…..$(i)$
Given equation can be re-written as
$9|x{|^2} – 19|x| + 2 = 0$
==> $(9|x| – 1)(|x| – 2) = 0$==> $|x| = 2$or $|x| = 1/9$
$\therefore$ Solution of the given equation are $ \pm \,2,\, \pm 1/9$
In the domain $(i),$ the required solutions are $ – 2,\, – 1/9$.
Standard 11
Mathematics
