Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2+45=0\)
2. \(-3(4x^2+6)=-(18x^2-36)\)
3. \(-x^2-16=0\)
4. \(13x^2-1146=5x^2+6\)
5. \(-2x^2+288=0\)
6. \(6x^2+123=8x^2-5\)
7. \(-8x^2+288=0\)
8. \(-3x^2-2=5x^2-10\)
9. \(7x^2-448=0\)
10. \(7x^2-112=0\)
11. \(-5(-9x^2+8)=-(-46x^2+36)\)
12. \(10x^2-239=8x^2+3\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2+45=0 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
2. \(-3(4x^2+6)=-(18x^2-36) \\ \Leftrightarrow -12x^2-18=-18x^2+36 \\ \Leftrightarrow -12x^2+18x^2=36+18 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(-x^2-16=0 \\ \Leftrightarrow -x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(13x^2-1146=5x^2+6 \\ \Leftrightarrow 13x^2-5x^2=6+1146 \\ \Leftrightarrow 8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
5. \(-2x^2+288=0 \\ \Leftrightarrow -2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(6x^2+123=8x^2-5 \\ \Leftrightarrow 6x^2-8x^2=-5-123 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(-8x^2+288=0 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(-3x^2-2=5x^2-10 \\ \Leftrightarrow -3x^2-5x^2=-10+2 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(7x^2-448=0 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
10. \(7x^2-112=0 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-5(-9x^2+8)=-(-46x^2+36) \\ \Leftrightarrow 45x^2-40=46x^2-36 \\ \Leftrightarrow 45x^2-46x^2=-36+40 \\ \Leftrightarrow -x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{-1} < 0 \\ V = \varnothing \\ -----------------\)
12. \(10x^2-239=8x^2+3 \\ \Leftrightarrow 10x^2-8x^2=3+239 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)