1. | a. | 4x2
- 12x = 0 4x(x - 3) = 0 x = 0 ∨ x = 3 |
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b. | 4 + 12x2
= 8x + 4 12x2 - 8x = 0 4x(3x - 2) = 0 4x = 0 ∨ 3x - 2 = 0 x = 0 ∨ x = 2/3 |
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c. | 3x2
- 4x
= 8x - 2x2 3x2 - 4x - 8x + 2x2 = 0 5x2- 12x = 0 x(5x - 12) = 0 x = 0 ∨ x = 12/5 |
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d. | 2x(x + 1) = 6x2
2x2 + 2x = 6x2 2x2 + 2x - 6x2 = 0 -4x2 + 2x = 0 2x(-2x + 1) = 0 2x = 0 ∨ -2x + 1 = 0 x = 0 ∨ x = 1/2 |
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e. | 4x2 + x(x
- 1) = 5x 4x2 + x2 - x = 5x 4x2 + x2 - x - 5x = 0 5x2 - 6x = 0 x(5x - 6) = 0 x = 0 ∨ 5x - 6 = 0 x = 0 ∨ x = 6/5 |
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f. | (x
- 3)2 + 1 =
8x + 10 (x - 3)(x - 3) + 1 = 8x + 10 x2 - 3x - 3x + 9 + 1 = 8x + 10 x2 - 3x - 3x + 9 + 1 - 8x - 10 = 0 x2 - 14x = 0 x(x - 14) = 0 x = 0 ∨ x = 14 |
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2. | a. | 2x3
- 10x = 0 2x(x2 - 5) = 0 2x = 0 ∨ x2 - 5 = 0 x = 0 ∨ x2 = 5 x = 0 ∨ x = √5 ∨ x = -√5 |
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b. | x4
- 8x2 = 0 x2(x2 - 8) = 0 x2 = 0 ∨ x2 - 8 = 0 x = 0 ∨ x2 = 8 x = 0 ∨ x = √8 ∨ x = -√8 |
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