Q. If $x$ satisfies $\left| x^{2} - 3x + 2 \right| + |x - 1| = x - 3$, then
A) $x \in \varnothing$
B) $x \in \lbrack 1,\ 2\rbrack$
C) $x \in \lbrack 3,\ \infty\rbrack$
D) $x \in ( - \infty,\ \infty)$
Explanation
(a)
We have, $\left| x^{2} - 3x + 2 \right| + |x - 1| = x - 3$
Therefore $x \geq 3$
$\therefore\ \ x^{2} - 3x + 2 + x - 1 = x - 3$
$\Rightarrow \ \ x^{2} - 3x + 4 = 0$
$\Rightarrow \ \ \left( x - \frac{3}{2} \right)^{2} = - \frac{7}{4}$
Hence, no solution exist
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.