{ x ∈ R:|x - 2|,, = {x^2}} =

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4-2.Quadratic Equations and Inequations

easy

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

A

$\{ -1, 2\}$

B

$\{1, 2\}$

C

$\{ -1, -2\}$

D

$\{1, -2\}$

Solution

(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$.

Standard 11

Mathematics

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