Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+8=0\)
2. \(6x^2+96=0\)
3. \(-3x^2+432=0\)
4. \(-4x^2+4=0\)
5. \(-2x^2-392=0\)
6. \(16x^2-52=10x^2+2\)
7. \(-9x^2+1022=-3x^2+8\)
8. \(-3(8x^2-8)=-(27x^2-51)\)
9. \(9x^2-5=6x^2-5\)
10. \(6x^2+150=0\)
11. \(-15x^2+1185=-9x^2+9\)
12. \(7x^2-1372=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+8=0 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(6x^2+96=0 \\ \Leftrightarrow 6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-3x^2+432=0 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
4. \(-4x^2+4=0 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-2x^2-392=0 \\ \Leftrightarrow -2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(16x^2-52=10x^2+2 \\ \Leftrightarrow 16x^2-10x^2=2+52 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(-9x^2+1022=-3x^2+8 \\ \Leftrightarrow -9x^2+3x^2=8-1022 \\ \Leftrightarrow -6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{-6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(-3(8x^2-8)=-(27x^2-51) \\ \Leftrightarrow -24x^2+24=-27x^2+51 \\ \Leftrightarrow -24x^2+27x^2=51-24 \\ \Leftrightarrow 3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(9x^2-5=6x^2-5 \\ \Leftrightarrow 9x^2-6x^2=-5+5 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(6x^2+150=0 \\ \Leftrightarrow 6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-15x^2+1185=-9x^2+9 \\ \Leftrightarrow -15x^2+9x^2=9-1185 \\ \Leftrightarrow -6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(7x^2-1372=0 \\ \Leftrightarrow 7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)