Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.5 Junior Find the answer

For which of the following values of $x$ is $x$ greater than $x^{2}$ : $x=-2$ , $x=-\frac{1}{2}$ , $x=0$ , $x=\frac{1}{2}$ , $x=2$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

When $x=-2$ , we get $x^{2}=4$ . Here, $x<x^{2}$ . When $x=-\frac{1}{2}$ , we get $x^{2}=\frac{1}{4}$ . Here, $x<x^{2}$ . When $x=0$ , we get $x^{2}=0$ . Here, $x=x^{2}$ . When $x=\frac{1}{2}$ , we get $x^{2}=\frac{1}{4}$ . Here, $x>x^{2}$ . When $x=2$ , we get $x^{2}=4$ . Here, $x<x^{2}$ . This means that $x=\frac{1}{2}$ is the only choice where $x>x^{2}$ .

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