Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2+2=0\)
2. \(4x^2-158=-2x^2-8\)
3. \(-9x^2-399=-7x^2-7\)
4. \(-3(-2x^2+2)=-(-2x^2+490)\)
5. \(8x^2+1152=0\)
6. \(3(8x^2+4)=-(-18x^2+42)\)
7. \(5(-8x^2+10)=-(45x^2-770)\)
8. \(-11x^2-843=-6x^2+2\)
9. \(-8x^2+22=-9x^2-3\)
10. \(11x^2-286=5x^2+8\)
11. \(-6x^2+54=0\)
12. \(-9x^2+121=-4x^2-4\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2+2=0 \\ \Leftrightarrow 2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(4x^2-158=-2x^2-8 \\ \Leftrightarrow 4x^2+2x^2=-8+158 \\ \Leftrightarrow 6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
3. \(-9x^2-399=-7x^2-7 \\ \Leftrightarrow -9x^2+7x^2=-7+399 \\ \Leftrightarrow -2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-3(-2x^2+2)=-(-2x^2+490) \\ \Leftrightarrow 6x^2-6=2x^2-490 \\ \Leftrightarrow 6x^2-2x^2=-490+6 \\ \Leftrightarrow 4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(8x^2+1152=0 \\ \Leftrightarrow 8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3(8x^2+4)=-(-18x^2+42) \\ \Leftrightarrow 24x^2+12=18x^2-42 \\ \Leftrightarrow 24x^2-18x^2=-42-12 \\ \Leftrightarrow 6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5(-8x^2+10)=-(45x^2-770) \\ \Leftrightarrow -40x^2+50=-45x^2+770 \\ \Leftrightarrow -40x^2+45x^2=770-50 \\ \Leftrightarrow 5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
8. \(-11x^2-843=-6x^2+2 \\ \Leftrightarrow -11x^2+6x^2=2+843 \\ \Leftrightarrow -5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{-5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-8x^2+22=-9x^2-3 \\ \Leftrightarrow -8x^2+9x^2=-3-22 \\ \Leftrightarrow x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(11x^2-286=5x^2+8 \\ \Leftrightarrow 11x^2-5x^2=8+286 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(-6x^2+54=0 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(-9x^2+121=-4x^2-4 \\ \Leftrightarrow -9x^2+4x^2=-4-121 \\ \Leftrightarrow -5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{-5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)