Aim: How do we solve radical equations?

Slides:

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Presentation transcript:

Aim: How do we solve radical equations? Do Now: Solve for x: 1. x + 1 = 5 2. x + 1 = -5 3. 4.

An equation in which a variable occurs in the radicand 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 √ x + 1 - 5 √ x + 1 = 5 (√ x + 1 )2 = (5)2 √ 24 + 1 - 5 5 - 5 x + 1 = 25 x = 24 Therefore, the solution is x = 24.

Therefore, there are no real roots. √ 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.

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

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.

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.

x - 3 = 0 or x - 7 = 0 x = 3 or x = 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.

You must square the whole side NOT each term. 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

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

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