Download presentation

Published byRodrigo Becking Modified over 4 years ago

1
**Warm up 1. Solve 2. Solve 3. Decompose to partial fractions -1/2, 1**

-1, -2 x<-2 or -1<x<5 Warm up

2
**Lesson 4-7 Radical Equations and Inequalities**

Objective: To solve radical equations and inequalities

3
**A radical equation contains a variable within a radical**

A radical equation contains a variable within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a power.

4
Remember! For a square root, the index of the radical is 2.

5
**Example 1 Solve . Original equation**

Solve Radical Equations Solve Original equation Add 1 to each side to isolate the radical. Square each side to eliminate the radical. Find the squares. Add 2 to each side. Example 1

6
**Example 1 Check Original equation Replace y with 38. Simplify. **

Solve Radical Equations Check Original equation Replace y with 38. ? Simplify. Answer: The solution checks. The solution is 38. Example 1

7
**Raising each side of an equation to an even power may introduce extraneous solutions.**

You can use the intersect feature on a graphing calculator to find the point where the two curves intersect. Helpful Hint

8
**Example 2 Method 1 Use algebra to solve the equation.**

Step 1 Solve for x. Square both sides. Simplify. 2x + 14 = x2 + 6x + 9 0 = x2 + 4x – 5 Factor. 0 = (x + 5)(x – 1) Write in standard form. Solve for x. x + 5 = 0 or x – 1 = 0 x = –5 or x = 1 Example 2

9
**Example 2 Method 1 Use algebra to solve the equation.**

Step 2 Use substitution to check for extraneous solutions. –2 x Because x = –5 is extraneous, the only solution is x = 1. Example 2

10
**Example 2 Solve the equation. Method 2 Use a graphing calculator.**

Let Y1 = and Y2 = x +3. The graphs intersect in only one point, so there is exactly one solution. The solution is x = 1. Example 2

11
Solve -75 Practice

12
Solve: 8, (24 does not work in the original equation) Practice

13
A radical inequality is an inequality that contains a variable within a radical. You can solve radical inequalities by graphing or using algebra. A radical expression with an even index and a negative radicand has no real roots. Remember!

14
**Example 3 Solve . Method 1 Use algebra to solve the inequality.**

Step 1 Solve for x. Subtract 2. Square both sides. Simplify. x – 3 ≤ 9 Solve for x. x ≤ 12 Example 3

15
**Example 3 Method 1 Use algebra to solve the inequality.**

Step 2 Consider the radicand. x – 3 ≥ 0 The radicand cannot be negative. x ≥ 3 Solve for x. The solution of is x ≥ 3 and x ≤ 12, or 3 ≤ x ≤ 12. Example 3

16
**Example 3 Solve . Method 2 Use a graph and a table.**

On a graphing calculator, let Y1 = and Y2 = 5. The graph of Y1 is at or below the graph of Y2 for values of x between 3 and 12. Notice that Y1 is undefined when < 3. The solution is 3 ≤ x ≤ 12. Example 3

17
**Example 4 Method 1 Use algebra to solve the inequality.**

Step 1 Solve for x. Cube both sides. x + 2 ≥ 1 Solve for x. x ≥ –1 Example 4

18
**Example 4 Method 1 Use algebra to solve the inequality.**

Step 2 Consider the radicand. x + 2 ≥ 1 The radicand cannot be negative. x ≥ –1 Solve for x. The solution of is x ≥ –1. Example 4

19
**Example 4 Solve . Method 1 Use a graph and a table.**

On a graphing calculator, let Y1 = and Y2 = 1. The graph of Y1 is at or above the graph of Y2 for values of x greater than –1. Notice that Y1 is undefined when < –2. The solution is x ≥ –1. Example 4

20
Solve x>7/2 Practice

21
Holt Algebra 2 Glencoe Algebra 2 Sources

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google