Q 17 - Precalculus Enhanced with Graphing Utilities

Question

Use a graphing utility to approximate the solutions of each equation rounded to two decimal places. All solutions lie between $-10$ and $10$.

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

Step-by-Step Solution

Answer

The required approximated solutions of the given equation are :- 

$-1.144 and 1.643$.

Step 1. Given Information

We have given the following equation :- 

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

We have to solve this equation, by using graphic utility.

Firstly we will draw the two curves for left and right side expressions of the given equation.

The intersecting points of these curves will be the solution.

Step 2. Draw graphs

Given Equation is :-

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

Let :-

$$\begin{gathered} Y_1=x^4-3 and \\ {Y}_2=2x+1 \end{gathered}$$

Now draw graph of both of these expressions on a single window using graphing utility as following :-

Step 3. Approximate Solutions

In the following graph of given function :- 

We know that solution exists, where both graphs cuts each other.

So the values of $x$ for that graphs cut each other, are the solutions of given equation.

So the approximate solutions of the given equation are :-

$-1.144 and 1.643$