# How do you solve x^2+1<2x using a sign chart?

Jan 9, 2017

The solution is $S = \left\{\emptyset\right\}$

#### Explanation:

Let's rewrite the inequality

${x}^{2} + 1 < 2 x$

${x}^{2} - 2 x + 1 < 0$

${\left(x - 1\right)}^{2} < 0$

This is impossible since

${\left(x - 1\right)}^{2} > 0$, $\forall x \in \mathbb{R}$