Warm-Up Find the inverse: 1.3y = 12x 2 + 9 2.f(x) = ½x + 8.

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Presentation transcript:

Warm-Up Find the inverse: 1.3y = 12x f(x) = ½x + 8

Section 6-6 Solve Radical Equations

Solving Radical Equations Radical equation: An equation with radicals that have variables in their radicands. Step 1: Isolate the radical on one side of the equation. Step 2: Raise each side of the equation to the same power to eliminate the radical. Step 3: Solve the equation.

Example 1 Solve: √5x – 9 = 11 ( ) 2 ( ) 2 5x = 130 5x – 9 = 121 x= 26 Step 1: Square both sides. Step 2: Solve for x.

Example 2 Solve: 7x 3/5 = 56 ( ) 5/3 ( ) 5/3 x 3/5 = x= 32 Step 1: Divide both sides by 7. Step 2: Raise each side to the power of 5 / 3. Step 3: Solve for x.

Example 3 Solve: (x – 4) 2/3 – 9 = 16 [ ] 3/2 ( ) 3/2 (x – 4) 2/3 = x – 4 = 125 Step 1: Add 9 to both sides. Step 2: Raise each side to the power of 3 / 2. Step 3: Solve for x. x = 129

Example 4 Solve: Check for extraneous solutions. √x – 6 = x – 8 ( ) 2 ( ) 2 x – 6 = x 2 – 16x + 64 x – 6 = (x – 8)(x – 8) x 2 – 17x + 70 = 0 Step 1: Square both sides. Step 2: FOIL the right side of the equation. Step 3: Set the equation equal to zero. (x – 10)(x – 7) = 0 Step 4: Factor. Step 5: Solve for x. x = 10 x = 7

Example 4 – C0ntinued Solve: Check for extraneous solutions. √x – 6 = x – 8 √10 – 6 = 10 – 8 2 = 2 Step 6: Check for extraneous roots. x = 10 x = 10 x = 7 √7 – 6 = 7 – 8 1 = -1

Homework Section 6-6 Pages 456 –459 1, 3, 4, 7, 12, 13, 16, , 28, 29, 34, 35, 37, 38, 43, 45, 47, 49, 63 – 65, 75, 78