Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2+128=0\)
2. \(-3(-7x^2+7)=-(-16x^2-959)\)
3. \(-4(8x^2+9)=-(37x^2-284)\)
4. \(-4(10x^2-10)=-(37x^2-40)\)
5. \(-2(-8x^2-4)=-(-10x^2-8)\)
6. \(-7x^2+0=0\)
7. \(5(10x^2-3)=-(-45x^2+15)\)
8. \(-6x^2-216=0\)
9. \(3(8x^2-4)=-(-21x^2-135)\)
10. \(4(-10x^2-5)=-(39x^2+69)\)
11. \(5x^2-125=0\)
12. \(-6x^2+1350=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2+128=0 \\ \Leftrightarrow -8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-3(-7x^2+7)=-(-16x^2-959) \\ \Leftrightarrow 21x^2-21=16x^2+959 \\ \Leftrightarrow 21x^2-16x^2=959+21 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-4(8x^2+9)=-(37x^2-284) \\ \Leftrightarrow -32x^2-36=-37x^2+284 \\ \Leftrightarrow -32x^2+37x^2=284+36 \\ \Leftrightarrow 5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-4(10x^2-10)=-(37x^2-40) \\ \Leftrightarrow -40x^2+40=-37x^2+40 \\ \Leftrightarrow -40x^2+37x^2=40-40 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-2(-8x^2-4)=-(-10x^2-8) \\ \Leftrightarrow 16x^2+8=10x^2+8 \\ \Leftrightarrow 16x^2-10x^2=8-8 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-7x^2+0=0 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(5(10x^2-3)=-(-45x^2+15) \\ \Leftrightarrow 50x^2-15=45x^2-15 \\ \Leftrightarrow 50x^2-45x^2=-15+15 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-6x^2-216=0 \\ \Leftrightarrow -6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{-6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(3(8x^2-4)=-(-21x^2-135) \\ \Leftrightarrow 24x^2-12=21x^2+135 \\ \Leftrightarrow 24x^2-21x^2=135+12 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(4(-10x^2-5)=-(39x^2+69) \\ \Leftrightarrow -40x^2-20=-39x^2-69 \\ \Leftrightarrow -40x^2+39x^2=-69+20 \\ \Leftrightarrow -x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{-1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(5x^2-125=0 \\ \Leftrightarrow 5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(-6x^2+1350=0 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)