7.3 Solving Radical Equations

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Presentation transcript:

7.3 Solving Radical Equations 𝑥 2/3 −5=7 𝑥 −7=𝑥+1 7.3 Solving Radical Equations Goal: Solve equations that contain radicals or rational exponents. 𝑥+4 = 𝑥+9 (2𝑥−3) 1/5 =6

Warm-up Evaluate the expression: 1. 2. Simplify: 3. Solve the equation: 4. 9 -4 9 -4

How to solve radical equations: A radical equation is an equation that contains radicals with the variable in the radicand. How to solve radical equations: Step 1 Isolate the radical on one side of the equation if necessary. Step 2 Raise each side of the equation to the same power to eliminate the radical. Step 3 Solve the resulting equation using techniques that you learned in previous chapters Step 4 Check your solution. This is extremely important because apparent solutions that do not work in the original equation are called extraneous. Extraneous solutions are not considered to be solutions of the problem. Solving Radical Equations:

Example 1: Solve: Check:

Examples: Solve and Check: Check:

Examples: Solve and Check: -4 3 Extraneous solution Check:

 Solve an Equation with Rational Exponents Add 9 to each side Raise each side to the Simplify Simplify Check 

Check:

Assignment Worksheet 7.3