Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2+567=0\)
2. \(-4x^2+8=-3x^2+8\)
3. \(5(-7x^2-9)=-(43x^2+77)\)
4. \(3(-9x^2-9)=-(23x^2-873)\)
5. \(8x^2-1568=0\)
6. \(-6x^2+1176=0\)
7. \(6x^2-13=2x^2-9\)
8. \(8x^2-648=0\)
9. \(-3(-8x^2+10)=-(-23x^2+26)\)
10. \(-4(-5x^2+3)=-(-24x^2+12)\)
11. \(4(-5x^2+2)=-(28x^2-808)\)
12. \(-2x^2+315=2x^2-9\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2+567=0 \\ \Leftrightarrow -7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{-7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(-4x^2+8=-3x^2+8 \\ \Leftrightarrow -4x^2+3x^2=8-8 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(5(-7x^2-9)=-(43x^2+77) \\ \Leftrightarrow -35x^2-45=-43x^2-77 \\ \Leftrightarrow -35x^2+43x^2=-77+45 \\ \Leftrightarrow 8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(3(-9x^2-9)=-(23x^2-873) \\ \Leftrightarrow -27x^2-27=-23x^2+873 \\ \Leftrightarrow -27x^2+23x^2=873+27 \\ \Leftrightarrow -4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{-4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(8x^2-1568=0 \\ \Leftrightarrow 8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(-6x^2+1176=0 \\ \Leftrightarrow -6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(6x^2-13=2x^2-9 \\ \Leftrightarrow 6x^2-2x^2=-9+13 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(8x^2-648=0 \\ \Leftrightarrow 8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(-3(-8x^2+10)=-(-23x^2+26) \\ \Leftrightarrow 24x^2-30=23x^2-26 \\ \Leftrightarrow 24x^2-23x^2=-26+30 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-4(-5x^2+3)=-(-24x^2+12) \\ \Leftrightarrow 20x^2-12=24x^2-12 \\ \Leftrightarrow 20x^2-24x^2=-12+12 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(4(-5x^2+2)=-(28x^2-808) \\ \Leftrightarrow -20x^2+8=-28x^2+808 \\ \Leftrightarrow -20x^2+28x^2=808-8 \\ \Leftrightarrow 8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(-2x^2+315=2x^2-9 \\ \Leftrightarrow -2x^2-2x^2=-9-315 \\ \Leftrightarrow -4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{-4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)