Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-7=-8x^2-3\)
2. \(-3(-10x^2+6)=-(-22x^2-54)\)
3. \(3x^2+3=0\)
4. \(5(-8x^2-9)=-(33x^2-522)\)
5. \(-7x^2-41=-8x^2+8\)
6. \(x^2+25=0\)
7. \(3(-9x^2-4)=-(22x^2-233)\)
8. \(3x^2+51=2x^2+2\)
9. \(5x^2-405=0\)
10. \(5x^2-1125=0\)
11. \(-4x^2+676=0\)
12. \(-4x^2-484=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-7=-8x^2-3 \\ \Leftrightarrow -4x^2+8x^2=-3+7 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
2. \(-3(-10x^2+6)=-(-22x^2-54) \\ \Leftrightarrow 30x^2-18=22x^2+54 \\ \Leftrightarrow 30x^2-22x^2=54+18 \\ \Leftrightarrow 8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(3x^2+3=0 \\ \Leftrightarrow 3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5(-8x^2-9)=-(33x^2-522) \\ \Leftrightarrow -40x^2-45=-33x^2+522 \\ \Leftrightarrow -40x^2+33x^2=522+45 \\ \Leftrightarrow -7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{-7} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-7x^2-41=-8x^2+8 \\ \Leftrightarrow -7x^2+8x^2=8+41 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(x^2+25=0 \\ \Leftrightarrow x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(3(-9x^2-4)=-(22x^2-233) \\ \Leftrightarrow -27x^2-12=-22x^2+233 \\ \Leftrightarrow -27x^2+22x^2=233+12 \\ \Leftrightarrow -5x^2 = 245 \\ \Leftrightarrow x^2 = \frac{245}{-5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(3x^2+51=2x^2+2 \\ \Leftrightarrow 3x^2-2x^2=2-51 \\ \Leftrightarrow x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5x^2-405=0 \\ \Leftrightarrow 5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(5x^2-1125=0 \\ \Leftrightarrow 5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(-4x^2+676=0 \\ \Leftrightarrow -4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{-4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-4x^2-484=0 \\ \Leftrightarrow -4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{-4} < 0 \\ V = \varnothing \\ -----------------\)