Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2+1790=5x^2-10\)
2. \(3x^2-3=0\)
3. \(3(-7x^2+2)=-(27x^2+858)\)
4. \(-3(10x^2+4)=-(29x^2+13)\)
5. \(-2(7x^2-2)=-(16x^2-292)\)
6. \(2(-9x^2+7)=-(25x^2-14)\)
7. \(-7x^2+1183=0\)
8. \(5(7x^2-8)=-(-41x^2+1054)\)
9. \(-3x^2+0=0\)
10. \(5x^2-77=-3x^2-5\)
11. \(-2x^2+72=0\)
12. \(13x^2-670=10x^2+5\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2+1790=5x^2-10 \\ \Leftrightarrow -3x^2-5x^2=-10-1790 \\ \Leftrightarrow -8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(3x^2-3=0 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(3(-7x^2+2)=-(27x^2+858) \\ \Leftrightarrow -21x^2+6=-27x^2-858 \\ \Leftrightarrow -21x^2+27x^2=-858-6 \\ \Leftrightarrow 6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{6} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-3(10x^2+4)=-(29x^2+13) \\ \Leftrightarrow -30x^2-12=-29x^2-13 \\ \Leftrightarrow -30x^2+29x^2=-13+12 \\ \Leftrightarrow -x^2 = -1 \\ \Leftrightarrow x^2 = \frac{-1}{-1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-2(7x^2-2)=-(16x^2-292) \\ \Leftrightarrow -14x^2+4=-16x^2+292 \\ \Leftrightarrow -14x^2+16x^2=292-4 \\ \Leftrightarrow 2x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(2(-9x^2+7)=-(25x^2-14) \\ \Leftrightarrow -18x^2+14=-25x^2+14 \\ \Leftrightarrow -18x^2+25x^2=14-14 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-7x^2+1183=0 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(5(7x^2-8)=-(-41x^2+1054) \\ \Leftrightarrow 35x^2-40=41x^2-1054 \\ \Leftrightarrow 35x^2-41x^2=-1054+40 \\ \Leftrightarrow -6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{-6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-3x^2+0=0 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(5x^2-77=-3x^2-5 \\ \Leftrightarrow 5x^2+3x^2=-5+77 \\ \Leftrightarrow 8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(-2x^2+72=0 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(13x^2-670=10x^2+5 \\ \Leftrightarrow 13x^2-10x^2=5+670 \\ \Leftrightarrow 3x^2 = 675 \\ \Leftrightarrow x^2 = \frac{675}{3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)