Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+16=0\)
2. \(7x^2-567=0\)
3. \(-5x^2+20=0\)
4. \(11x^2+579=7x^2+3\)
5. \(8x^2+0=0\)
6. \(2x^2+66=5x^2-9\)
7. \(7x^2+1372=0\)
8. \(3x^2-442=-4x^2+6\)
9. \(x^2-16=0\)
10. \(-x^2+16=0\)
11. \(-4x^2+9=3x^2+9\)
12. \(-4(-9x^2+10)=-(-30x^2+190)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+16=0 \\ \Leftrightarrow x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(7x^2-567=0 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
3. \(-5x^2+20=0 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
4. \(11x^2+579=7x^2+3 \\ \Leftrightarrow 11x^2-7x^2=3-579 \\ \Leftrightarrow 4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(8x^2+0=0 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(2x^2+66=5x^2-9 \\ \Leftrightarrow 2x^2-5x^2=-9-66 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(7x^2+1372=0 \\ \Leftrightarrow 7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(3x^2-442=-4x^2+6 \\ \Leftrightarrow 3x^2+4x^2=6+442 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(x^2-16=0 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
10. \(-x^2+16=0 \\ \Leftrightarrow -x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-4x^2+9=3x^2+9 \\ \Leftrightarrow -4x^2-3x^2=9-9 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-4(-9x^2+10)=-(-30x^2+190) \\ \Leftrightarrow 36x^2-40=30x^2-190 \\ \Leftrightarrow 36x^2-30x^2=-190+40 \\ \Leftrightarrow 6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{6} < 0 \\ V = \varnothing \\ -----------------\)