Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2-8=-4x^2-8\)
2. \(5x^2+94=9x^2-6\)
3. \(-8x^2+5=-5x^2+5\)
4. \(-x^2+100=0\)
5. \(-2(-10x^2+7)=-(-14x^2+14)\)
6. \(-x^2+16=0\)
7. \(-2x^2-8=4x^2-8\)
8. \(3(6x^2-8)=-(-15x^2-339)\)
9. \(x^2+144=0\)
10. \(-2(-9x^2+10)=-(-14x^2+20)\)
11. \(-2(8x^2-8)=-(19x^2-28)\)
12. \(-x^2+518=7x^2+6\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2-8=-4x^2-8 \\ \Leftrightarrow -6x^2+4x^2=-8+8 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(5x^2+94=9x^2-6 \\ \Leftrightarrow 5x^2-9x^2=-6-94 \\ \Leftrightarrow -4x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
3. \(-8x^2+5=-5x^2+5 \\ \Leftrightarrow -8x^2+5x^2=5-5 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-x^2+100=0 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(-2(-10x^2+7)=-(-14x^2+14) \\ \Leftrightarrow 20x^2-14=14x^2-14 \\ \Leftrightarrow 20x^2-14x^2=-14+14 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-x^2+16=0 \\ \Leftrightarrow -x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-2x^2-8=4x^2-8 \\ \Leftrightarrow -2x^2-4x^2=-8+8 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(3(6x^2-8)=-(-15x^2-339) \\ \Leftrightarrow 18x^2-24=15x^2+339 \\ \Leftrightarrow 18x^2-15x^2=339+24 \\ \Leftrightarrow 3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(x^2+144=0 \\ \Leftrightarrow x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2(-9x^2+10)=-(-14x^2+20) \\ \Leftrightarrow 18x^2-20=14x^2-20 \\ \Leftrightarrow 18x^2-14x^2=-20+20 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-2(8x^2-8)=-(19x^2-28) \\ \Leftrightarrow -16x^2+16=-19x^2+28 \\ \Leftrightarrow -16x^2+19x^2=28-16 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-x^2+518=7x^2+6 \\ \Leftrightarrow -x^2-7x^2=6-518 \\ \Leftrightarrow -8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{-8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)