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CEMC Fermat, 2021

Algebra Difficulty 1.2 Junior Find the answer Canada

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, $\text{x lt; x 2}$ .

When $x=-\frac{1}{2}$ , we get $x^2 = \frac{1}{4}$ . Here, $\text{x lt; x 2}$ .

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, $\text{x gt; x 2}$ .

When $x=2$ , we get $x^2 = 4$ . Here, $\text{x lt; x 2}$ .

This means that $x=\frac{1}{2}$ is the only choice where $\text{x gt;x 2}$ .

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