Chapter 4.6, Problem 83AYU

The inequality $x^4+1<-5$ has no solution. Explain why.

To determine

To find: The inequality $x^4 +1< -5$ has no real solution. Explain why.

Answer to Problem 83AYU

Solution:

$x^4 < -6$, the square value can never be negative, so there is no solution to the inequality.

Explanation of Solution

Given:

The inequality $x^4 +1< -5$.

Calculation:

$x^4 +1< -5$ has no real solution.

Subtract $-1$ on both sides we get $x^4<-6$, the square value never be negative, so there is no solution to the inequality.