Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(4x^2+9)=-(20x^2-621)\)
2. \(8x^2-128=0\)
3. \(6x^2+0=0\)
4. \(2x^2+50=0\)
5. \(3(-7x^2-3)=-(15x^2+159)\)
6. \(11x^2+24=6x^2+4\)
7. \(5x^2+42=8x^2-6\)
8. \(-10x^2+850=-3x^2+3\)
9. \(5(10x^2-6)=-(-58x^2+230)\)
10. \(-9x^2-85=-6x^2-10\)
11. \(-2(-6x^2-6)=-(-5x^2+1563)\)
12. \(-3x^2+588=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(4x^2+9)=-(20x^2-621) \\ \Leftrightarrow -12x^2-27=-20x^2+621 \\ \Leftrightarrow -12x^2+20x^2=621+27 \\ \Leftrightarrow 8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(8x^2-128=0 \\ \Leftrightarrow 8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
3. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(2x^2+50=0 \\ \Leftrightarrow 2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(3(-7x^2-3)=-(15x^2+159) \\ \Leftrightarrow -21x^2-9=-15x^2-159 \\ \Leftrightarrow -21x^2+15x^2=-159+9 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(11x^2+24=6x^2+4 \\ \Leftrightarrow 11x^2-6x^2=4-24 \\ \Leftrightarrow 5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5x^2+42=8x^2-6 \\ \Leftrightarrow 5x^2-8x^2=-6-42 \\ \Leftrightarrow -3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{-3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-10x^2+850=-3x^2+3 \\ \Leftrightarrow -10x^2+3x^2=3-850 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(5(10x^2-6)=-(-58x^2+230) \\ \Leftrightarrow 50x^2-30=58x^2-230 \\ \Leftrightarrow 50x^2-58x^2=-230+30 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(-9x^2-85=-6x^2-10 \\ \Leftrightarrow -9x^2+6x^2=-10+85 \\ \Leftrightarrow -3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{-3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-2(-6x^2-6)=-(-5x^2+1563) \\ \Leftrightarrow 12x^2+12=5x^2-1563 \\ \Leftrightarrow 12x^2-5x^2=-1563-12 \\ \Leftrightarrow 7x^2 = -1575 \\ \Leftrightarrow x^2 = \frac{-1575}{7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-3x^2+588=0 \\ \Leftrightarrow -3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{-3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)