Chapter 1, Equations and Graphs - Section 1.9 - Solving Equations and Inequalities Graphically - 1.9 Exercises - Page 158: 32

$x=\left\{-2.31, 1.79\right\}$.

Work Step by Step

To solve the given equation graphically, perform the following steps: (1) Graph the functions $y=x^4$ (red graph) and $y=16-x^3$ (blue graph) using a graphing utility. Refer to the image below for the graph. (2) Identify the point/s where the graphs intersect each other. These are the points where the value of $x^4$ and $16-x^3$ are equal. The x-coordinates of these points are the solutions to the given equation. Notice that the graphs intersect each other at $(-2.306, 28.255)$ and $(1.79, 10.265)$. This means that the solutions to the given equation are: $-2.306$, and $1.79$. Thus, the solutions, rounded to two decimal places when needed, are: $x=\left\{-2.31, 1.79\right\}$.

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