If |x² - 3x + 2| > x² - 3x + 2, then which one of the following is correct?

Question

Question

This question was previously asked in

NDA (Held On: 17 Nov 2019) Maths Previous Year paper

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Answer 1

Concept:

If f (x) = |x|, then \(f\left( x \right) = \;\left\{ {\begin{array}{*{20}{c}} {x\;,\;x \ge 0}\\ { - x,\;x < 0} \end{array}} \right.\)

Calculation:

Given: |x² - 3x + 2| > x² - 3x + 2

Case-1: If x ≥ 0

⇒ x² - 3x + 2 > x² - 3x + 2

∴ No real value of x satisfies the above equation.

Case-2:- If x < 0

⇒ - (x² - 3x + 2) > x² - 3x + 2

⇒ x² - 3x + 2 < 0

⇒ (x - 1) (x - 2) < 0

⇒ 1 < x < 2.