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| 1. | a. | √(2x - 1) -
√(x - 4) = 2 (√(2x - 1) - √(x - 4))2 = 4 2x - 1 - 2 • (√(2x - 1)•√(x - 4)) + x - 4 = 4 2 • (√(2x - 1)•√(x - 4)) = 4 - 2x + 1 - x + 4 2 • (√(2x - 1)•√(x - 4)) = 9 - 3x 4(2x - 1)(x - 4) = (9 - 3x)2 4(2x2 - 8x - x + 4) = 81 - 54x + 9x2 8x2 - 36x + 16 = 81 - 54x + 9x2 0 = x2 - 18x + 65 0 = (x - 5)(x - 13) x = 5 ∨ x = 13 controleren: beide oplossingen voldoen. |
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| b. | 2√x =
√(x - 3) + √(3x - 3) 4x = (√(x - 3) + √(3x - 3))2 4x = x - 3 + 2 • √(x - 3)•√(3x - 3) + 3x - 3 4x - x + 3 - 3x + 3 = 2 • √(x - 3)•√(3x - 3) 6 = 2•√(x - 3)•√(3x - 3) 3 = √(x - 3)•√(3x - 3) 9 = (x - 3)(3x- 3) 9 = 3x2 - 9x - 3x + 9 0 = 3x2 - 12x 0 = 3x(x - 4) x = 0 ∨ x = 4 controleren: x = 4 voldoet. |
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| c. | √(x + 7) + 2 =
√(3 - x) (√(x + 7) + 2)2 = 3 - x x + 7 + 2•√(x + 7)•2 + 4 = 3 - x 4√(x + 7) = 3 - x - x - 7 - 4 4√(x + 7) = -2x - 8 16(x + 7) = (-2x - 8)2 16x + 112 = 4x2 + 2•2x•8 + 64 16x + 112 = 4x2 + 32x + 64 0 = 4x2 + 16x - 48 0 = x2 + 4x - 12 0 = (x - 2)(x + 6) x = 2 ∨ x = -6 controleren x = -6 voldoet |
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© h.hofstede (h.hofstede@hogeland.nl) |
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