Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2+72=0\)
2. \(-16x^2-1007=-10x^2+7\)
3. \(2(4x^2+6)=-(-x^2-579)\)
4. \(8x^2-32=0\)
5. \(2x^2+164=4x^2+2\)
6. \(-5x^2-20=0\)
7. \(-5x^2+500=0\)
8. \(-5x^2-405=0\)
9. \(-7x^2+567=0\)
10. \(-3x^2+192=0\)
11. \(3(9x^2-2)=-(-22x^2-14)\)
12. \(-x^2+25=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2+72=0 \\ \Leftrightarrow 8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-16x^2-1007=-10x^2+7 \\ \Leftrightarrow -16x^2+10x^2=7+1007 \\ \Leftrightarrow -6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{-6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2(4x^2+6)=-(-x^2-579) \\ \Leftrightarrow 8x^2+12=x^2+579 \\ \Leftrightarrow 8x^2-x^2=579-12 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(8x^2-32=0 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
5. \(2x^2+164=4x^2+2 \\ \Leftrightarrow 2x^2-4x^2=2-164 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-5x^2-20=0 \\ \Leftrightarrow -5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{-5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-5x^2+500=0 \\ \Leftrightarrow -5x^2 = -500 \\ \Leftrightarrow x^2 = \frac{-500}{-5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(-5x^2-405=0 \\ \Leftrightarrow -5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{-5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-7x^2+567=0 \\ \Leftrightarrow -7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{-7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-3x^2+192=0 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(3(9x^2-2)=-(-22x^2-14) \\ \Leftrightarrow 27x^2-6=22x^2+14 \\ \Leftrightarrow 27x^2-22x^2=14+6 \\ \Leftrightarrow 5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-x^2+25=0 \\ \Leftrightarrow -x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{-1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)