Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2-450=0\)
2. \(-5(-5x^2+5)=-(-22x^2+22)\)
3. \(2(10x^2-9)=-(-19x^2-46)\)
4. \(x^2-792=5x^2-8\)
5. \(-6x^2+1350=0\)
6. \(4(-8x^2+6)=-(30x^2+138)\)
7. \(-3(-8x^2-4)=-(-31x^2-859)\)
8. \(6x^2+216=0\)
9. \(-2x^2-450=0\)
10. \(3x^2-192=0\)
11. \(2x^2+72=0\)
12. \(4x^2-100=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2-450=0 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(-5(-5x^2+5)=-(-22x^2+22) \\ \Leftrightarrow 25x^2-25=22x^2-22 \\ \Leftrightarrow 25x^2-22x^2=-22+25 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(2(10x^2-9)=-(-19x^2-46) \\ \Leftrightarrow 20x^2-18=19x^2+46 \\ \Leftrightarrow 20x^2-19x^2=46+18 \\ \Leftrightarrow x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(x^2-792=5x^2-8 \\ \Leftrightarrow x^2-5x^2=-8+792 \\ \Leftrightarrow -4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{-4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-6x^2+1350=0 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(4(-8x^2+6)=-(30x^2+138) \\ \Leftrightarrow -32x^2+24=-30x^2-138 \\ \Leftrightarrow -32x^2+30x^2=-138-24 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(-3(-8x^2-4)=-(-31x^2-859) \\ \Leftrightarrow 24x^2+12=31x^2+859 \\ \Leftrightarrow 24x^2-31x^2=859-12 \\ \Leftrightarrow -7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{-7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(6x^2+216=0 \\ \Leftrightarrow 6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-2x^2-450=0 \\ \Leftrightarrow -2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{-2} < 0 \\ V = \varnothing \\ -----------------\)
10. \(3x^2-192=0 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(2x^2+72=0 \\ \Leftrightarrow 2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4x^2-100=0 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)