Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2+123=4x^2+2\)
2. \(-5x^2-720=0\)
3. \(-2(-10x^2-8)=-(-18x^2-258)\)
4. \(-3x^2-192=0\)
5. \(9x^2+12=2x^2+5\)
6. \(6x^2-1176=0\)
7. \(7x^2-112=0\)
8. \(-2(-9x^2+2)=-(-14x^2+260)\)
9. \(12x^2-120=10x^2+8\)
10. \(-4x^2+484=0\)
11. \(5(-6x^2-7)=-(31x^2+35)\)
12. \(5(-2x^2-10)=-(15x^2+895)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2+123=4x^2+2 \\ \Leftrightarrow 3x^2-4x^2=2-123 \\ \Leftrightarrow -x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{-1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(-5x^2-720=0 \\ \Leftrightarrow -5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{-5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-2(-10x^2-8)=-(-18x^2-258) \\ \Leftrightarrow 20x^2+16=18x^2+258 \\ \Leftrightarrow 20x^2-18x^2=258-16 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(-3x^2-192=0 \\ \Leftrightarrow -3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(9x^2+12=2x^2+5 \\ \Leftrightarrow 9x^2-2x^2=5-12 \\ \Leftrightarrow 7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{7} < 0 \\ V = \varnothing \\ -----------------\)
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. \(7x^2-112=0 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-2(-9x^2+2)=-(-14x^2+260) \\ \Leftrightarrow 18x^2-4=14x^2-260 \\ \Leftrightarrow 18x^2-14x^2=-260+4 \\ \Leftrightarrow 4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{4} < 0 \\ V = \varnothing \\ -----------------\)
9. \(12x^2-120=10x^2+8 \\ \Leftrightarrow 12x^2-10x^2=8+120 \\ \Leftrightarrow 2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
10. \(-4x^2+484=0 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(5(-6x^2-7)=-(31x^2+35) \\ \Leftrightarrow -30x^2-35=-31x^2-35 \\ \Leftrightarrow -30x^2+31x^2=-35+35 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(5(-2x^2-10)=-(15x^2+895) \\ \Leftrightarrow -10x^2-50=-15x^2-895 \\ \Leftrightarrow -10x^2+15x^2=-895+50 \\ \Leftrightarrow 5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{5} < 0 \\ V = \varnothing \\ -----------------\)