Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2+72=6x^2-3\)
2. \(11x^2-717=6x^2+3\)
3. \(7x^2-847=0\)
4. \(9x^2+47=10x^2-2\)
5. \(-3(8x^2-7)=-(28x^2-21)\)
6. \(3x^2-300=0\)
7. \(5(6x^2+9)=-(-22x^2-77)\)
8. \(-2x^2+72=0\)
9. \(-3(4x^2-8)=-(17x^2-1149)\)
10. \(-4x^2+796=4x^2-4\)
11. \(x^2-4=0\)
12. \(-4(-5x^2-10)=-(-14x^2-904)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2+72=6x^2-3 \\ \Leftrightarrow 3x^2-6x^2=-3-72 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
2. \(11x^2-717=6x^2+3 \\ \Leftrightarrow 11x^2-6x^2=3+717 \\ \Leftrightarrow 5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(7x^2-847=0 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(9x^2+47=10x^2-2 \\ \Leftrightarrow 9x^2-10x^2=-2-47 \\ \Leftrightarrow -x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{-1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
5. \(-3(8x^2-7)=-(28x^2-21) \\ \Leftrightarrow -24x^2+21=-28x^2+21 \\ \Leftrightarrow -24x^2+28x^2=21-21 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(3x^2-300=0 \\ \Leftrightarrow 3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(5(6x^2+9)=-(-22x^2-77) \\ \Leftrightarrow 30x^2+45=22x^2+77 \\ \Leftrightarrow 30x^2-22x^2=77-45 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(-2x^2+72=0 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
9. \(-3(4x^2-8)=-(17x^2-1149) \\ \Leftrightarrow -12x^2+24=-17x^2+1149 \\ \Leftrightarrow -12x^2+17x^2=1149-24 \\ \Leftrightarrow 5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(-4x^2+796=4x^2-4 \\ \Leftrightarrow -4x^2-4x^2=-4-796 \\ \Leftrightarrow -8x^2 = -800 \\ \Leftrightarrow x^2 = \frac{-800}{-8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
11. \(x^2-4=0 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-4(-5x^2-10)=-(-14x^2-904) \\ \Leftrightarrow 20x^2+40=14x^2+904 \\ \Leftrightarrow 20x^2-14x^2=904-40 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)