Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+98=0\)
2. \(-4(4x^2+10)=-(21x^2-805)\)
3. \(5x^2-320=0\)
4. \(3x^2-4=2x^2-3\)
5. \(14x^2-568=10x^2+8\)
6. \(4(-3x^2+10)=-(4x^2+1112)\)
7. \(x^2+0=0\)
8. \(6x^2-384=0\)
9. \(3x^2-569=-4x^2-2\)
10. \(3(3x^2-4)=-(-13x^2+268)\)
11. \(-x^2+196=0\)
12. \(14x^2-26=9x^2-6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+98=0 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(-4(4x^2+10)=-(21x^2-805) \\ \Leftrightarrow -16x^2-40=-21x^2+805 \\ \Leftrightarrow -16x^2+21x^2=805+40 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(5x^2-320=0 \\ \Leftrightarrow 5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(3x^2-4=2x^2-3 \\ \Leftrightarrow 3x^2-2x^2=-3+4 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(14x^2-568=10x^2+8 \\ \Leftrightarrow 14x^2-10x^2=8+568 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(4(-3x^2+10)=-(4x^2+1112) \\ \Leftrightarrow -12x^2+40=-4x^2-1112 \\ \Leftrightarrow -12x^2+4x^2=-1112-40 \\ \Leftrightarrow -8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
7. \(x^2+0=0 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(6x^2-384=0 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(3x^2-569=-4x^2-2 \\ \Leftrightarrow 3x^2+4x^2=-2+569 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(3(3x^2-4)=-(-13x^2+268) \\ \Leftrightarrow 9x^2-12=13x^2-268 \\ \Leftrightarrow 9x^2-13x^2=-268+12 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(-x^2+196=0 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(14x^2-26=9x^2-6 \\ \Leftrightarrow 14x^2-9x^2=-6+26 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)