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4-2.Quadratic Equations and Inequations
normal
Number of positive integral values of $'K'$ for which the equation $k = \left| {x + \left| {2x - 1} \right|} \right| - \left| {x - \left| {2x - 1} \right|} \right|$ has exactly three real solutions, is
A
$0$
B
$2$
C
$3$
D
$5$
Solution
$\left| {x + \left| {2x – 1} \right|} \right| – \left| {x – \left| {2x – 1} \right|} \right| = 2Min\left( {x,\left| {2x – 1} \right|} \right)$
$|2 x-1|=x$
$\therefore 2 x-1=\pm x$
$x=1, \frac{1}{3}$
at $x=\frac{1}{3}$
$\mathrm{k}=\left|\frac{1}{3}+\frac{1}{3}\right|=\frac{2}{3}$
Standard 11
Mathematics
