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| 1. | a. | x3 - 3x2
= 0 x2(x - 3) = 0 x2 = 0 ∨ x - 3 = 0 x = 0 ∨ x = 3 |
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| b. | 4x5 + 2x6
= 0 2x5(2 + x) = 0 2x5 = 0 ∨ 2 + x = 0 x = 0 ∨ x = -2 |
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| c. | x7 = 4x5
x7 - 4x5 = 0 x5(x2 - 4) = 0 x5 = 0 ∨ x2 - 4 = 0 x = 0 ∨ x2 = 4 x = 0 ∨ x = 2 ∨ x = -2 |
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| d. | x7 - 243x2
= 0 x2(x5 - 243) = 0 x2 = 0 ∨ x5 - 243 = 0 x = 0 ∨ x5 = 243 x = 0 ∨ x = 3 |
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| e. | x8 = 125x5 x8 - 125x5 = 0 x5(x3 - 125) = 0 x5 = 0 ∨ x3 - 125 = 0 x = 0 ∨ x3 = 125 x = 0 ∨ x = 5 |
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| f. | 6x2 = 4x9 6x2 - 4x9 = 0 2x2 (3 - 2x7 ) = 0 2x2 = 0 ∨ 3 - 2x7 = 0 x2 = 0 ∨ 2x7 = 3 x = 0 ∨ x7 = 1,5 x = 0 ∨ x = (1,5)1/7 = 1,06 |
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| g. | x7 =
5x7 - x5 x7 - 5x7 + x5 = 0 -4x7 + x5 = 0 x5 (-4x2 + 1) = 0 x5 = 0 ∨ -4x2 + 1 = 0 x = 0 ∨ 4x2 = 1 x = 0 ∨ x2 = 1/4 x = 0 ∨ x = 1/2 ∨ x = -1/2 |
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| h. | 17x8 - x6 =
x8 17x8 - x6 - x8 = 0 16x8 - x6 = 0 x6(16x2 - 1) = 0 x6 = 0 ∨ 16x2 - 1 = 0 x = 0 ∨ 16x2 = 1 x = 0 ∨ x2 = 1/16 x = 0 ∨ x = 1/4 ∨ x = -1/4 |
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| i. | 3x4 + x7 =
x4 + 5x7 3x4 + x7 - x4 - 5x7 = 0 2x4 - 4x7 = 0 2x4 (1 - 2x3) = 0 2x4 = 0 ∨ 1 - 2x3 = 0 x4 = 0 ∨ 2x3 = 1 x = 0 ∨ x3 = 0,5 x = 0 ∨ x = 0,51/3 = 0,79 |
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| j. | x2(x2 +
x5) = 5x7 x4 + x7 - 5x7 = 0 x4 - 4x7 = 0 x4 (1 - 4x3) = 0 x4 = 0 ∨ 1 - 4x3 = 0 x = 0 ∨ 1 = 4x3 x = 0 ∨ x3 = 0,25 x = 0 ∨ x = 0,251/3 = 0,63 |
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| 2. | a. | x4 + 7x3
+ 10x2 = 0 x2 (x2 + 7x + 10) = 0 x2 = 0 ∨ x2 + 7x + 10 = 0 x = 0 ∨ (x + 5)(x + 2) = 0 x = 0 ∨ x = -5 ∨ x = -2 |
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| b. | x3 = 2x2
+ 15x x3 - 2x2 - 15x = 0 x(x2 - 2x - 15) = 0 x = 0 ∨ x2 - 2x - 15 = 0 x = 0 ∨ (x - 5)(x + 3) = 0 x = 0 ∨ x = 5 ∨ x = -3 |
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| c. | 4x5 - 12x3
= 8x4 4x5 - 8x4 - 12x3 = 0 4x3 (x2 - 2x - 3) = 0 4x3 = 0 ∨ x2 - 2x- 3 = 0 x3 = 0 ∨ (x - 3)(x + 1) = 0 x = 0 ∨ x = 3 ∨ x = -1 |
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| d. | x - 5√x
= 0 √x(√x - 5) = 0 √x = 0 ∨ √x - 5 = 0 x = 0 ∨ √x = 5 x = 0 ∨ x = 25 |
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| e. | x8 = x7
+ 6x6 x8 - x7 - 6x6 = 0 x6 (x2 - x - 6) = 0 x6 = 0 ∨ x2 - x - 6 = 0 x = 0 ∨ (x - 3)(x + 2) = 0 x = 0 ∨ x = 3 ∨ x = -2 |
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| f. | x - √x = 5√x x - √x - 5√x = 0 x - 6√x √x(√x - 6) = 0 √x = 0 ∨ √x - 6 = 0 x = 0 ∨ √x = 6 x = 0 ∨ x = 36 |
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| g. | x2√x
- 2x√x = 24√x x2√x - 2x√x - 24√x = 0 √x(x2 - 2x - 24) = 0 √x = 0 ∨ x2 - 2x - 24 = 0 x = 0 ∨ (x - 6)(x + 4) = 0 x = 0 ∨ x = 6 ∨ x = -4 Maar die -4 valt af, want √-4 bestaat niet. |
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| h. | x6 + 3x5
= 10x4 x6 + 3x5 - 10x4 = 0 x4 (x2 + 3x - 10) = 0 x4 = 0 ∨ x2 + 3x- 10 = 0 x = 0 ∨ (x - 2)(x + 5) = 0 x = 0 ∨ x = 2 ∨ x = -5 |
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| 3. | a. | x = 0 geeft
y = 44 44 = -x3 + 27x + 44 -x3 + 27x = 0 x(-x2 + 27) = 0 x = 0 ∨ -x2 + 27 = 0 x = 0 ∨ x2 = 27 x = 0 ∨ x = √27 Ú x = -√27 P en R zijn de punten (√27, 44) en (-√27, 44) De afstand daartussen is 2√27 = 10,39 |
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| b. | (x + 4)(p + 4x - x2
) = px + 4x2 - x3 + 4p + 16x - 4x2 = -x3 + x(p + 16) + 4p dat moet gelijk zijn aan -x3 + 27x + 44 dus moet gelden p + 16 = 27 en 4p = 44 dat klopt inderdaad beiden voor p = 11 |
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© h.hofstede (h.hofstede@hogeland.nl) |
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