Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-5x^2-10)=-(19x^2+200)\)
2. \(8x^2-32=0\)
3. \(3(-6x^2-5)=-(21x^2+15)\)
4. \(5(-10x^2+8)=-(46x^2-824)\)
5. \(2x^2+41=7x^2-4\)
6. \(4x^2+13=10x^2+7\)
7. \(-3x^2+0=0\)
8. \(3(2x^2+9)=-(-3x^2-54)\)
9. \(2x^2-450=0\)
10. \(6x^2-864=0\)
11. \(-3x^2+12=0\)
12. \(5x^2+402=9x^2+2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-5x^2-10)=-(19x^2+200) \\ \Leftrightarrow -25x^2-50=-19x^2-200 \\ \Leftrightarrow -25x^2+19x^2=-200+50 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
2. \(8x^2-32=0 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(3(-6x^2-5)=-(21x^2+15) \\ \Leftrightarrow -18x^2-15=-21x^2-15 \\ \Leftrightarrow -18x^2+21x^2=-15+15 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(5(-10x^2+8)=-(46x^2-824) \\ \Leftrightarrow -50x^2+40=-46x^2+824 \\ \Leftrightarrow -50x^2+46x^2=824-40 \\ \Leftrightarrow -4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{-4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2x^2+41=7x^2-4 \\ \Leftrightarrow 2x^2-7x^2=-4-41 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(4x^2+13=10x^2+7 \\ \Leftrightarrow 4x^2-10x^2=7-13 \\ \Leftrightarrow -6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{-6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(-3x^2+0=0 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(3(2x^2+9)=-(-3x^2-54) \\ \Leftrightarrow 6x^2+27=3x^2+54 \\ \Leftrightarrow 6x^2-3x^2=54-27 \\ \Leftrightarrow 3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(2x^2-450=0 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(6x^2-864=0 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(-3x^2+12=0 \\ \Leftrightarrow -3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{-3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(5x^2+402=9x^2+2 \\ \Leftrightarrow 5x^2-9x^2=2-402 \\ \Leftrightarrow -4x^2 = -400 \\ \Leftrightarrow x^2 = \frac{-400}{-4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)