|x-2|=x2⇒x-2=x2 or 2-x=x2 ⇒x2-x+2=0 or x2+x-2=0⇒x2+x-2=0 [∵x2-x+2=0 does not gives any real root] ⇒(x+2)(x-1)=0⇒x=-2,1.

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

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${- 1, 2}$

${1, 2}$

${- 1, - 2}$

${1, - 2}$

answer is D.

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Detailed Solution

$| x - 2 | = x^{2} \Rightarrow x - 2 = x^{2} or 2 - x = x^{2} \Rightarrow x^{2} - x + 2 = 0 or x^{2} + x - 2 = 0 \Rightarrow x^{2} + x - 2 = 0 [∵ x^{2} - x + 2 = 0 does not gives any real root] \Rightarrow (x + 2) (x - 1) = 0 \Rightarrow x = - 2, 1 .$