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Prentice Hall Lesson 11.5 EQ: How do you solve a radical equation?

Prentice Hall Lesson 11.5 EQ: How do you solve a radical equation?. BOP:. Solution to BOP:. ALGEBRA 1 LESSON 11-4. 10 5. 47. 8 2 units 50. 6 10 units 52. Answers may vary. Sample: 8 2 + 4 3, 2 7 + 9 3, 6 5 + 3 7

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Prentice Hall Lesson 11.5 EQ: How do you solve a radical equation?

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  1. Prentice Hall Lesson 11.5EQ: How do you solve a radical equation? BOP:

  2. Solution to BOP:

  3. ALGEBRA 1 LESSON 11-4 10 5 • 47. • 8 2 units • 50. 6 10 units • 52. Answers may vary. Sample: • 8 2 + 4 3, 2 7 + 9 3, • 6 5 + 3 7 • 53. a. The student simplified 48 • as 2 24 instead of 2 12 • or 4 3. • b. 2 6 + 4 3 • 54.a. 2 2 or 2.8 ft • b.s 2 37. 7.4 ft 38. 5 10 41. 8 + 2 15 44. –24 11-4

  4. ALGEBRA 1 LESSON 11-4 9 2 2 ab b 55. 9.1% 56. 12.8% 57. 15.5% 58.a.x b.xx 59. 60. about 251 years 61. They are unlike radicals. 62.a. 1, 0, 1, 1; 4, 1, 5, 17; 5, 3, 8, 34; 8, 6, 14, 10; 10, 9, 19, 181 b. No; the only values it worked for were 0 and 1. • 63. a + b ≠≠ a + b • 64. • 67. 2 • 70 • 71.a. 2 6 • b. 2 13 • c. 2(p + q) n 2 n – 1 2 11-4

  5. Prentice Hall Lesson 11.5EQ: How do you solve a radical equation? Toolbox: Radical equation – an equation with a variable in a radicand. To solve a radical equation, isolate the radical using inverse operations. Then square both sides and solve for the variable. To solve radical equations with radical expressions on both sides, square both sides of the equation. Then use inverse operations to solve for the variable.

  6. Extraneous solution – a solution that does not satisfy the original equation. • ALWAYS check your solutions to determine whether a solution is extraneous. If the only solution you get after checking your work is extraneous, then the original equation has no solution.

  7. ALGEBRA 1 LESSON 11-5 a.x – 5 = 4 x = 9 Isolate the radical on the left side of the equation. ( x)2 = 92Square each side. 4 = 4 Solve each equation. Check your answers. x = 81 Check: x – 5 = 4 81 – 5 4 Substitute 81 for x. 9 – 5 4 11-5

  8. ALGEBRA 1 LESSON 11-5 ( x – 5)2 = 42 Square each side. Check: x – 5 = 4 21– 5 = 4 Substitute 21 for x. 16 = 4 4 = 4 (continued) b.x – 5 = 4 x – 5 = 16 Solve for x. x = 21 11-5

  9. ALGEBRA 1 LESSON 11-5 On a roller coaster ride, your speed in a loop depends on the height of the hill you have just come down and the radius of the loop in feet. The equation v = 8 h – 2r gives the velocity v in feet per second of a car at the top of the loop. 11-5

  10. ALGEBRA 1 LESSON 11-5 Solve v = 8 h – 2r for h when v = 120 and r = 18. 120 = 8 h – 2(18) Substitute 120 for v and 18 for r. (15)2 = ( h – 36)2 Square both sides. 120 8 8 h – 2(18) 8 = Divide each side by 8 to isolate the radical. 15 = h – 36 Simplify. (continued) The loop on a roller coaster ride has a radius of 18 ft. Your car has a velocity of 120 ft/s at the top of the loop. How high is the hill of the loop you have just come down before going into the loop? 225 = h – 36 261 = h The hill is 261 ft high. 11-5

  11. ALGEBRA 1 LESSON 11-5 Solve 3x – 4 = 2x + 3. ( 3x – 4)2 = ( 2x + 3)2Square both sides. Check: 3x – 4 = 2x + 3 3(7) – 4 2(7) + 3 Substitute 7 for x. 17 = 17 3x – 4 = 2x + 3 Simplify. 3x = 2x + 7 Add 4 to each side. x = 7 Subtract 2x from each side. The solution is 7. 11-5

  12. ALGEBRA 1 LESSON 11-5 Solve x = x + 12. (x)2 = ( x + 12)2Square both sides. Check: x = x + 12 4 4 + 12 –3 –3 + 12 4 = 4 –3 = 3 / x2 = x + 12 x2 – x – 12 = 0 Simplify. (x – 4)(x + 3) = 0 Solve the quadratic equation by factoring. (x – 4) = 0 or (x + 3) = 0 Use the Zero–Product Property. x = 4  or   x = –3 Solve for x. The solution to the original equation is 4. The value –3 is an extraneous solution. 11-5

  13. ALGEBRA 1 LESSON 11-5 Solve 3x + 8 = 2. 3x = –6 ( 3x)2 = (–6)2Square both sides. Check: 3x + 8 = 2 3(12) + 8 2   Substitute 12 for x. 36 + 8 2 6 + 8 = 2   x = 12 does not solve the original equation. / 3x + 8 = 2 has no solution. 3x = 36 x = 12 11-5

  14. Solve each radical equation. 1. 7x – 3 = 4 2. 3x – 2 = x + 2 3. 2x + 7 = 5x – 8 4.x = 2x + 8 5. 3x + 4 + 5 = 3 5 7 2 Solving Radical Equations ALGEBRA 1 LESSON 11-5 2 5 4 no solution 11-5

  15. Summary: Don’t forget to write your minimum three sentence summary answering today’s essential question on your summary paper!

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