Chapter 3.5, Problem 20AYU

$25x^2\text{ + 16 < 40}x$

To determine

To find: The solution of the inequality $25x^2+16<40x$.

Answer to Problem 20AYU

Solution:

No real solution

Explanation of Solution

Given:

The inequality is $25x^2+16<40x$

Calculation:

$25x^2+16-40x<0$

$25x^2-40x+16<0$

${\left(5x-4\right)}^2<0$

Left hand side of the above inequality is ${\left(5x-4\right)}^2$; which is a perfect square.

So this cannot be less than zero.

Therefore the above inequality does not have any real solutions.