# How do you solve the inequality x^2<10x-25?

Jan 25, 2017

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

#### Explanation:

Let's factorise the inequality

${x}^{2} < 10 x - 25$

${x}^{2} - 10 x + 25 < 0$

$\left(x - 5\right) \left(x - 5\right) < 0$

${\left(x - 5\right)}^{2} < 0$

$\forall x \in \mathbb{R} ,$ $\implies$, ${\left(x - 5\right)}^{2} \ge 0$

Therefore,

There is no solution