Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-8x^2+5)=-(36x^2-696)\)
2. \(-4(-9x^2-2)=-(-34x^2-16)\)
3. \(x^2-81=0\)
4. \(-6x^2+150=0\)
5. \(16x^2+734=10x^2+8\)
6. \(3x^2-507=0\)
7. \(10x^2+187=6x^2-9\)
8. \(6x^2+54=0\)
9. \(-4x^2+256=0\)
10. \(2(3x^2-2)=-(0x^2-1010)\)
11. \(4x^2-1017=-3x^2-9\)
12. \(-4x^2+144=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-8x^2+5)=-(36x^2-696) \\ \Leftrightarrow -32x^2+20=-36x^2+696 \\ \Leftrightarrow -32x^2+36x^2=696-20 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
2. \(-4(-9x^2-2)=-(-34x^2-16) \\ \Leftrightarrow 36x^2+8=34x^2+16 \\ \Leftrightarrow 36x^2-34x^2=16-8 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(x^2-81=0 \\ \Leftrightarrow x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(-6x^2+150=0 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(16x^2+734=10x^2+8 \\ \Leftrightarrow 16x^2-10x^2=8-734 \\ \Leftrightarrow 6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3x^2-507=0 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(10x^2+187=6x^2-9 \\ \Leftrightarrow 10x^2-6x^2=-9-187 \\ \Leftrightarrow 4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(6x^2+54=0 \\ \Leftrightarrow 6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-4x^2+256=0 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
10. \(2(3x^2-2)=-(0x^2-1010) \\ \Leftrightarrow 6x^2-4=0x^2+1010 \\ \Leftrightarrow 6x^2+0x^2=1010+4 \\ \Leftrightarrow 6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(4x^2-1017=-3x^2-9 \\ \Leftrightarrow 4x^2+3x^2=-9+1017 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
12. \(-4x^2+144=0 \\ \Leftrightarrow -4x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{-4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)