Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.
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Transcript of Warm Up4-22-09 Solve each equation. 1. 3 x +5 = 17 2. 4 x + 1 = 2 x – 3 3.
Holt Algebra 1
11-9 Solving Radical Equations
Warm Up 4-22-09Solve each equation.1. 3x +5 = 172. 4x + 1 = 2x – 3 3. 4. (x + 7)(x – 4) = 05. x2 – 11x + 30 = 06. x2 = 2x + 15
4–2
35–7, 4 6, 5
5, –3
Holt Algebra 1
11-9 Solving Radical Equations
Solve radical equations.Objective
Holt Algebra 1
11-9 Solving Radical Equations
radical equationextraneous solution
Vocabulary
Holt Algebra 1
11-9 Solving Radical Equations
A radical equation is an equation that contains a variable within a radical. In this course, you will only study radical equations that contain square roots.
Recall that you use inverse operations to solve equations. For nonnegative numbers, squaring and taking the square root are inverse operations. When an equation contains a variable within a square root, square both sides of the equation to solve.
Holt Algebra 1
11-9 Solving Radical Equations
Holt Algebra 1
11-9 Solving Radical Equations
Directions: Solve the equation. Check your answer.
Holt Algebra 1
11-9 Solving Radical EquationsExample 1
x = 25
55 5
Check
Holt Algebra 1
11-9 Solving Radical EquationsExample 2
100 = 2x50 = x
Check
10 10
Holt Algebra 1
11-9 Solving Radical EquationsExample 3
3x = 1
Check
Holt Algebra 1
11-9 Solving Radical Equations
Some square-root equations do not have the square root isolated. To solve these equations, you may have to isolate the square root before squaring both sides. You can do this by using one or more inverse operations.
Holt Algebra 1
11-9 Solving Radical EquationsExample 4
x = 81Check
9 – 4 55 5
Holt Algebra 1
11-9 Solving Radical EquationsExample 5
x = 46Check
7 7
Holt Algebra 1
11-9 Solving Radical EquationsExample 6
5x + 1 = 165x = 15
x = 3
Holt Algebra 1
11-9 Solving Radical EquationsExample 6 Continued
4 + 6 1010 10
Check
Holt Algebra 1
11-9 Solving Radical EquationsExample 7
Method 1
x = 64
Holt Algebra 1
11-9 Solving Radical EquationsExample 7 Continued
Method 2
x = 64
Holt Algebra 1
11-9 Solving Radical EquationsExample 7 Continued
32 32
Check
Holt Algebra 1
11-9 Solving Radical EquationsExample 8
Method 1
144 = x
Holt Algebra 1
11-9 Solving Radical EquationsExample 8 Continued
Method 2
144 = x
Holt Algebra 1
11-9 Solving Radical EquationsExample 8 Continued
12 12
Check
Holt Algebra 1
11-9 Solving Radical EquationsExample 9
Method 1
x = 100
Holt Algebra 1
11-9 Solving Radical EquationsExample 9 Continued
Method 2
4x = 400x = 100
Holt Algebra 1
11-9 Solving Radical EquationsExample 9 Continued
Check
4 4
4
Holt Algebra 1
11-9 Solving Radical EquationsLesson Summary
Solve each equation. Check your answer.
1.
3.
2.
4.
36 45
no solution 11