Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-7x^2+9)=-(17x^2-18)\)
2. \(-2x^2+1340=-8x^2-10\)
3. \(x^2+169=0\)
4. \(3(-6x^2+8)=-(21x^2+24)\)
5. \(4x^2+4=0\)
6. \(11x^2-5=9x^2-5\)
7. \(8x^2-968=0\)
8. \(15x^2-1018=9x^2-4\)
9. \(13x^2-57=9x^2+7\)
10. \(6x^2+864=0\)
11. \(-x^2-669=-5x^2+7\)
12. \(-6x^2+384=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-7x^2+9)=-(17x^2-18) \\ \Leftrightarrow -14x^2+18=-17x^2+18 \\ \Leftrightarrow -14x^2+17x^2=18-18 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-2x^2+1340=-8x^2-10 \\ \Leftrightarrow -2x^2+8x^2=-10-1340 \\ \Leftrightarrow 6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(x^2+169=0 \\ \Leftrightarrow x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(3(-6x^2+8)=-(21x^2+24) \\ \Leftrightarrow -18x^2+24=-21x^2-24 \\ \Leftrightarrow -18x^2+21x^2=-24-24 \\ \Leftrightarrow 3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(4x^2+4=0 \\ \Leftrightarrow 4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(11x^2-5=9x^2-5 \\ \Leftrightarrow 11x^2-9x^2=-5+5 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(8x^2-968=0 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(15x^2-1018=9x^2-4 \\ \Leftrightarrow 15x^2-9x^2=-4+1018 \\ \Leftrightarrow 6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(13x^2-57=9x^2+7 \\ \Leftrightarrow 13x^2-9x^2=7+57 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
10. \(6x^2+864=0 \\ \Leftrightarrow 6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-x^2-669=-5x^2+7 \\ \Leftrightarrow -x^2+5x^2=7+669 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-6x^2+384=0 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)