x R:|x - 2| , , = x^2 = - Vidyadip

MCQ

$\{ x \in R:|x - 2|\,\, = {x^2}\} = $

A
$\{ -1, 2\}$
B
$\{1, 2\}$
C
$\{ -1, -2\}$
✓
$\{1, -2\}$

✓

Answer

Correct option: D.

$\{1, -2\}$

d
(d) $|x - 2|\, = {x^2}$$ \Rightarrow x - 2 = {x^2}$ or $2 - x = {x^2}$

$ \Rightarrow {x^2} - x + 2 = 0$ or ${x^2} + x - 2 = 0$ $ \Rightarrow {x^2} + x - 2 = 0$

$[\because \,{x^2} - x + 2 = 0$ does not gives any real root]

$ \Rightarrow (x + 2)(x - 1) = 0\,\,\, \Rightarrow x = - 2,\,1$.

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