Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2-75=0\)
2. \(8x^2+72=0\)
3. \(5x^2-720=0\)
4. \(6x^2-266=2x^2-10\)
5. \(-3x^2+300=0\)
6. \(2(-9x^2+5)=-(25x^2-185)\)
7. \(-6x^2-36=-8x^2-4\)
8. \(-5x^2+3=-6x^2+4\)
9. \(-3x^2+108=0\)
10. \(5x^2-605=0\)
11. \(-3x^2+48=0\)
12. \(-5(-3x^2+9)=-(-10x^2-80)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2-75=0 \\ \Leftrightarrow 3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
2. \(8x^2+72=0 \\ \Leftrightarrow 8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(5x^2-720=0 \\ \Leftrightarrow 5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
4. \(6x^2-266=2x^2-10 \\ \Leftrightarrow 6x^2-2x^2=-10+266 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(-3x^2+300=0 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(2(-9x^2+5)=-(25x^2-185) \\ \Leftrightarrow -18x^2+10=-25x^2+185 \\ \Leftrightarrow -18x^2+25x^2=185-10 \\ \Leftrightarrow 7x^2 = 175 \\ \Leftrightarrow x^2 = \frac{175}{7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(-6x^2-36=-8x^2-4 \\ \Leftrightarrow -6x^2+8x^2=-4+36 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-5x^2+3=-6x^2+4 \\ \Leftrightarrow -5x^2+6x^2=4-3 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-3x^2+108=0 \\ \Leftrightarrow -3x^2 = -108 \\ \Leftrightarrow x^2 = \frac{-108}{-3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
10. \(5x^2-605=0 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-3x^2+48=0 \\ \Leftrightarrow -3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{-3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(-5(-3x^2+9)=-(-10x^2-80) \\ \Leftrightarrow 15x^2-45=10x^2+80 \\ \Leftrightarrow 15x^2-10x^2=80+45 \\ \Leftrightarrow 5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)