Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2+0=0\)
2. \(9x^2-7=6x^2-4\)
3. \(2(2x^2+7)=-(-7x^2+94)\)
4. \(2(7x^2-2)=-(-6x^2-196)\)
5. \(-2x^2+9=2x^2+9\)
6. \(5(-4x^2-8)=-(28x^2-472)\)
7. \(-2(-9x^2-7)=-(-17x^2-10)\)
8. \(5(-4x^2+9)=-(18x^2+5)\)
9. \(-3x^2+22=2x^2+2\)
10. \(-5x^2+720=0\)
11. \(-3(10x^2+3)=-(35x^2-596)\)
12. \(6x^2-486=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2+0=0 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(9x^2-7=6x^2-4 \\ \Leftrightarrow 9x^2-6x^2=-4+7 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(2(2x^2+7)=-(-7x^2+94) \\ \Leftrightarrow 4x^2+14=7x^2-94 \\ \Leftrightarrow 4x^2-7x^2=-94-14 \\ \Leftrightarrow -3x^2 = -108 \\ \Leftrightarrow x^2 = \frac{-108}{-3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(2(7x^2-2)=-(-6x^2-196) \\ \Leftrightarrow 14x^2-4=6x^2+196 \\ \Leftrightarrow 14x^2-6x^2=196+4 \\ \Leftrightarrow 8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-2x^2+9=2x^2+9 \\ \Leftrightarrow -2x^2-2x^2=9-9 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(5(-4x^2-8)=-(28x^2-472) \\ \Leftrightarrow -20x^2-40=-28x^2+472 \\ \Leftrightarrow -20x^2+28x^2=472+40 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(-2(-9x^2-7)=-(-17x^2-10) \\ \Leftrightarrow 18x^2+14=17x^2+10 \\ \Leftrightarrow 18x^2-17x^2=10-14 \\ \Leftrightarrow x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5(-4x^2+9)=-(18x^2+5) \\ \Leftrightarrow -20x^2+45=-18x^2-5 \\ \Leftrightarrow -20x^2+18x^2=-5-45 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
9. \(-3x^2+22=2x^2+2 \\ \Leftrightarrow -3x^2-2x^2=2-22 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-5x^2+720=0 \\ \Leftrightarrow -5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{-5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(-3(10x^2+3)=-(35x^2-596) \\ \Leftrightarrow -30x^2-9=-35x^2+596 \\ \Leftrightarrow -30x^2+35x^2=596+9 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
12. \(6x^2-486=0 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)