Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(10x^2+6)=-(-13x^2-12)\)
2. \(-2(4x^2+3)=-(2x^2+300)\)
3. \(11x^2+43=10x^2-6\)
4. \(-8x^2+8=0\)
5. \(13x^2-1121=8x^2+4\)
6. \(-3(-2x^2-5)=-(-7x^2+10)\)
7. \(-17x^2-262=-10x^2-10\)
8. \(-4x^2+0=0\)
9. \(-5x^2-45=-7x^2+5\)
10. \(-6x^2+96=0\)
11. \(7x^2-567=0\)
12. \(-4x^2-5=-3x^2-5\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(10x^2+6)=-(-13x^2-12) \\ \Leftrightarrow 20x^2+12=13x^2+12 \\ \Leftrightarrow 20x^2-13x^2=12-12 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-2(4x^2+3)=-(2x^2+300) \\ \Leftrightarrow -8x^2-6=-2x^2-300 \\ \Leftrightarrow -8x^2+2x^2=-300+6 \\ \Leftrightarrow -6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{-6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(11x^2+43=10x^2-6 \\ \Leftrightarrow 11x^2-10x^2=-6-43 \\ \Leftrightarrow x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-8x^2+8=0 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(13x^2-1121=8x^2+4 \\ \Leftrightarrow 13x^2-8x^2=4+1121 \\ \Leftrightarrow 5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(-3(-2x^2-5)=-(-7x^2+10) \\ \Leftrightarrow 6x^2+15=7x^2-10 \\ \Leftrightarrow 6x^2-7x^2=-10-15 \\ \Leftrightarrow -x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{-1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(-17x^2-262=-10x^2-10 \\ \Leftrightarrow -17x^2+10x^2=-10+262 \\ \Leftrightarrow -7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{-7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-5x^2-45=-7x^2+5 \\ \Leftrightarrow -5x^2+7x^2=5+45 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(-6x^2+96=0 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(7x^2-567=0 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
12. \(-4x^2-5=-3x^2-5 \\ \Leftrightarrow -4x^2+3x^2=-5+5 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)