IM9A
Solving Radical Equations
Example 1: Solve the following equations involving square roots. Check your solutions to make sure
they make the original equation true.
Try to isolate the radicals first if possible.
Check: Example 2: Solve 5 𝑥 − 1 = 𝑥 + 1. Check your solution graphically.
Example 3: Solve the equation
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𝑥 − 2 = 2.
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Example 4: Solve (𝑥 − 5)! = 2. !
Rewrite as (𝑥 − 5)! = 2 Cube both sides of the equation. (𝑥 − 5)! = 8 Solve this quadratic equation by taking the square root of both sides 𝑥 − 5 = ±2 2 Don’t forget the ± !
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𝑥 = 5 ± 2 2 Check: (5 ± 2 2 − 5)! = (±2 2)! =
!
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(±2 2) =
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8 = 2 Exercises: Solve each of the following equations. Confirm your answers graphically or by plugging in your solutions back into the original Equation. Solutions: 1. 3𝑥 − 5 = 4 𝑥 = 7 2. 𝑥 + 5 − 1 = 0 𝑥 = −4 3. 𝑥 ! − 9 = 6 𝑥 = 3 5 4. 𝑥 + 14 − 3𝑥 − 10 = 0 𝑥 = 12 !
5. 4𝑥 − 1 = 3 𝑥 = 7 6. 𝑥 − 2 = 𝑥 − 2 + 12 𝑥 = 18 7. Consider the function 𝑓 𝑥 = 4 + 𝑥 − 3. a. Describe the transformations that would change the graph of 𝑦 = 𝑥 into the graph of 𝑓 𝑥 = 4 + 𝑥 − 3. b. What is the domain of 𝑓 𝑥 = 4 + 𝑥 − 3? c. The function 𝑓 𝑥 = 4 + 𝑥 − 3 does not have any zeros. Explain how you know without using a graph. d. Find the values of x such that 𝑓 𝑥 = 6.