1 / 10

Aim: How do we solve radical equations?

Aim: How do we solve radical equations?. Do Now : Solve for x : 1. x + 1 = 5 2. x + 1 = -5 3. 4. HW: p.112 # 16,18,22,24,26,28 p. 37 # 29,31 p.35 # 8 p.115 # 20. Radical Equations. An equation in which a variable occurs in the radicand

melora
Download Presentation

Aim: How do we solve radical equations?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Aim: How do we solve radical equations? • Do Now: Solve for x: • 1. x + 1 = 5 • 2. x + 1 = -5 • 3. • 4. HW: p.112 # 16,18,22,24,26,28 p. 37 # 29,31 p.35 # 8 p.115 # 20

  2. Radical Equations An equation in which a variable occurs in the radicand is called a radical equation. It should be noted, that when solving a radical equation algebraically, extraneous roots may be introduced when both sides of an equation are squared. Therefore, you must check your solutions for a radical equation. Check: L.S. R.S. Solve: √ x + 1 - 5 = 0 x ≥ 3 0 √ x + 1 - 5 √ x + 1 = 5 (√ x + 1 )2 = (5)2 √ 24 + 1 - 5 5 - 5 0 x + 1 = 25 x = 24 Therefore, the solution is x = 24.

  3. √ x + 1 + 5 = 0 Check: √ x + 1= - 5 (√ x + 1)2= (- 5)2 x + 1 = 25 x = 24 reject the answer x = 24 is extraneous. Therefore, there are no real roots.

  4. Solving Radical Equations 4 + √ 4 + x2 = x Check: x √ 4 + x2 = x - 4 (√ 4 + x2)2= (x - 4)2 4 + x2 = x2 - 8x + 16 8x = 12 Since the solution of is extraneous. Therefore, there are no real roots. x = ≠

  5. Solving Radical Equations Solve x ≥ -2 Set up the equation so that there will be one radical on each side of the equal sign. Square both sides. 2x + 4 = x + 7 x = 3 Simplify. L.S. R.S. Verify your solution. Therefore, the solution is x = 3.

  6. Solving Radical Equations Set up the equation so that there will be only one radical on each side of the equal sign. Solve Square both sides of the equation. Use Foil. Simplify. Simplify by dividing by a common factor of 2. Square both sides of the equation. Use Foil.

  7. Solving Radical Equations Distribute the 4. Simplify. Factor the quadratic. Solve for x. x - 3 = 0 or x - 7 = 0 x = 3 or x = 7 Verify both solutions. L.S. R.S. L.S. R.S.

  8. One more to see another extraneous solution: The radical is already isolated 2 2 Square both sides You must square the whole side NOT each term. This must be FOILed

  9. checks! Therefore, the solution is 8 only. Doesn't work!Extraneous Doesn't work!Extraneous

  10. Drill x = 2 1. 2. 3. 4. 5. x = 4 x = 2 x = 3 x = 2

More Related