Q. 8 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 5–16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between - 10 and 10. $-x^4 + 1 = 2x^2 - 3$

Step-by-Step Solution

Answer

The values of X are approximately 1.11 and -1.11.

Step 1. Given equation

$-x^4 + 1 = 2x^2 - 3$

Step 2. Simplify the equation

$$\begin{gathered} -x^4 + 1 = 2x^2 - 3 \\ \Rightarrow -x^4 + 1 - 2x^2 + 3=0 \\ \Rightarrow -x^4 - 2x^2 + 4=0 \end{gathered}$$

Step 4.Draw the graph and X-intercepts

x-intercepts are $x\approx 1.11178...x\approx -1.11178...$