Unit 7 Quadratics

Radical EquationsGoal: I can solve simple radical equations in one variable (A-REI.2)

Radical Equations-Radical Equations-

Extraneous Solutions-Extraneous Solutions-

An equation in which the An equation in which the variable is under a radicalvariable is under a radical

An answer that is generated when solving a An answer that is generated when solving a radical equation, but is radical equation, but is not a solutionnot a solution to the to the original equation.original equation.

VOCABULARY:

EXAMPLE 1: Solve the equation. Check for extraneous solutions

4x 2 2

16x 4x

16 4The opposite of a square root is squaring!

You must check for every problem!

EXAMPLE 2: Solve the equation. Check for extraneous solutions

2 6d 2 2

18d

2 36d 2 2

2 6d

2(18) 6

36 6

Your turn…

2 1 5x 2 2

13x

2 1 25x 1 1

2 1 5x

2( )13 1 5

26 1 5 2 26x 2 2 25 5

EXAMPLE 3: Solve the equation. Check for extraneous solutions

3 1 10g

2 2

9g

3g

1 1 3 9g 3 3

3 1 10g 3 9 1 10 3(3) 1 10 9 1 10

14n

EXAMPLE 4: Solve the equation. Check for extraneous solutions

3 2 12n

2 2

2 16n 2 2

2 4n 3 3

3 2 12n 3 114 2 2 3 16 12 3(4) 12 12 12

Extraneous Solution

60d

Your turn…

2 4 16d

2 2

4 64d 4 4

4 8d 2 2

2 4 16d 62 4 160

2 4 60 16 2 64 16

2 8 1660d

2 2

1x

EXAMPLE 5: Solve the equation. Check for extraneous solutions

3 1x x

x x 2 3 1x

3 1x x 3 1x x

11 13 2 2

2 2x 3 3

2 2

0x

Your turn…

8 3 8x x

3 3x x 2 8 8x

8 3 8x x 8 3 8x x

0 08 3 8 8 8

2 0x 8 8

2 2

14k

EXAMPLE 6: Solve the equation. Check for extraneous solutions

2 40 16 2 0k k

2 2k k 4 40 16k

2 40 16 2k k

2 40 16 2 0k k 28 40 16 28 0

12 12 0 4 56k 40 40

2 40 16 2k k

Your turn…

2 886

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Homework

Radical Equations (odds)