Chapter P, Problem 58RE

Solution

The solution of the given equation graphically.

  $x=-1,\text{ and }x=1.449$

Given information:

The inequality given is:

  $\left|2x-1\right|=4-x^2$ .

Formula used:

The solution of equation is graphically represented by the points where the curve of the equation intersects the x -axes.

Calculation:

In order to find the solution of the given equation

  $\left|2x-1\right|=4-x^2$

First rewrite it as:

  $\left|2x-1\right|-4+x^2=0$

First plot the graph of the function corresponding to the given equation, that is $f\left(x\right)=\left|2x-1\right|-4+x^2=0$

, using a calculator, as shown below:

  

Now, note that the curve of the function is intersecting x- axes only at two points, $x=-1,\text{ and }x=1.449$ that gives the solution of the equation $\left|2x-1\right|-4+x^2=0$ .

Thus, solution of given equation is:

  $x=-1,\text{ and }x=1.449$