Chapter 3.5, Problem 42AYU

Explain why the inequality $x^2-x\text{ + 1 < 0}$ has the empty set as the solution set.

To determine

To find: To prove the inequality $x^2-x+1<0$ has the empty set as the solution set.

Answer to Problem 42AYU

Solution:

$x^2-x+1<0$

$x^2+1<x$

The above inequality cannot be true for any real numbers $x$.

Therefore the given inequality has the empty set as the solution set.

Explanation of Solution

Given:

The inequality is: $x^2-x+1<0$

Calculation:

$x^2-x+1<0$

$x^2+1<x$

The above inequality cannot be true for any real numbers $x$.

Therefore the given inequality has the empty set as the solution set.