unit 7 quadratics radical equations goal: i can solve simple radical equations in one variable...
TRANSCRIPT
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
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
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
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