Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(8x^2-7)=-(-43x^2+35)\)
2. \(-x^2-1004=-7x^2+10\)
3. \(-10x^2+206=-6x^2+10\)
4. \(-2(-10x^2+3)=-(-19x^2+7)\)
5. \(2(-9x^2-4)=-(25x^2-692)\)
6. \(-2(-10x^2+9)=-(-16x^2+18)\)
7. \(-3x^2+108=0\)
8. \(-4(-2x^2-8)=-(-3x^2-32)\)
9. \(7x^2+196=10x^2+4\)
10. \(13x^2+14=9x^2-2\)
11. \(8x^2-1800=0\)
12. \(6x^2-600=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(8x^2-7)=-(-43x^2+35) \\ \Leftrightarrow 40x^2-35=43x^2-35 \\ \Leftrightarrow 40x^2-43x^2=-35+35 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-x^2-1004=-7x^2+10 \\ \Leftrightarrow -x^2+7x^2=10+1004 \\ \Leftrightarrow 6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(-10x^2+206=-6x^2+10 \\ \Leftrightarrow -10x^2+6x^2=10-206 \\ \Leftrightarrow -4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
4. \(-2(-10x^2+3)=-(-19x^2+7) \\ \Leftrightarrow 20x^2-6=19x^2-7 \\ \Leftrightarrow 20x^2-19x^2=-7+6 \\ \Leftrightarrow x^2 = -1 \\ \Leftrightarrow x^2 = \frac{-1}{1} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2(-9x^2-4)=-(25x^2-692) \\ \Leftrightarrow -18x^2-8=-25x^2+692 \\ \Leftrightarrow -18x^2+25x^2=692+8 \\ \Leftrightarrow 7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(-2(-10x^2+9)=-(-16x^2+18) \\ \Leftrightarrow 20x^2-18=16x^2-18 \\ \Leftrightarrow 20x^2-16x^2=-18+18 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-3x^2+108=0 \\ \Leftrightarrow -3x^2 = -108 \\ \Leftrightarrow x^2 = \frac{-108}{-3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(-4(-2x^2-8)=-(-3x^2-32) \\ \Leftrightarrow 8x^2+32=3x^2+32 \\ \Leftrightarrow 8x^2-3x^2=32-32 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(7x^2+196=10x^2+4 \\ \Leftrightarrow 7x^2-10x^2=4-196 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
10. \(13x^2+14=9x^2-2 \\ \Leftrightarrow 13x^2-9x^2=-2-14 \\ \Leftrightarrow 4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{4} < 0 \\ V = \varnothing \\ -----------------\)
11. \(8x^2-1800=0 \\ \Leftrightarrow 8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(6x^2-600=0 \\ \Leftrightarrow 6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)