Chapter 1, Problem 96RE

To determine

To calculate: The solution of the equation $\sqrt{x+4}=x^2-5$ graphically.

Answer to Problem 96RE

The solution of the equation $\sqrt{x+4}=x^2-5$ are $x=-2.5\text{ and }x=2.7$ .

Explanation of Solution

Given information:

The equation is $\sqrt{x+4}=x^2-5$

Calculation:

Consider the equation $\sqrt{x+4}=x^2-5$ .

Divide the above equation in two parts.

Follow the steps provided below to estimate the solution of the equation,

Step 1: Press $Y=$ key, enter the function $Y_1=\sqrt{X+4}$ .

Step 2: Enter the function $Y_2=X^2-5$ .

Step 3: Press the $\text{TRACE}$ key.

Step 4: Press $\text{2nd}$ key and then $\text{TRACE}$ key.

Step 5: Choose the 5^th option that is the intersect feature.

Step 6: Press $\text{ENTER}$ key to select both the functions.

Step 7: Guess the intersect point and press $\text{ENTER}$ key.

The result obtained on screen is provided below,

  

The graphs intersect at $\left(-2.5,1.2\right)$ .

Step 8: Press $\text{2nd}$ key and then $\text{TRACE}$ key.

Step 9: Choose the 5^th option that is the intersect feature.

Step 10: Press $\text{ENTER}$ key to select both the functions.

Step 11: Guess the intersect point and press $\text{ENTER}$ key.

The result obtained on screen is provided below,

  

The graphs intersect at $\left(2.7,2.5\right)$ .

There are two points of intersection that depict the solution of the equation.

Thus, the solution of the equation $\sqrt{x+4}=x^2-5$ are $x=-2.5\text{ and }x=2.7$ .