How do you solve the inequality $x > x^{2}$ $x>x^2$ and write your answer in interval notation?

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Answer 1 · 2017-02-14T15:07:04

$x < 0 and > 1$ $x < 0 and > 1$

$x = x^{2} = x (1 - x) > 0$ $x=x^2=x(1-x)>0$ .

So, x and (1-x) have the same sign.

When $x > 1$ $x > 1$ , both are positive.

When $x < 0$ $x < 0$ , both are negative,

When $x \in (0, 1)$ $x in (0, 1)$ , they have opposite signs.

How do you solve the inequality x>x2x>x^2 and write your answer in interval notation?