Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(2x^2+8)=-(-16x^2+254)\)
2. \(-2(6x^2+3)=-(15x^2+198)\)
3. \(15x^2+9=7x^2+9\)
4. \(2(5x^2-4)=-(-14x^2+24)\)
5. \(-5x^2-7=-8x^2-7\)
6. \(-5x^2+30=-8x^2+3\)
7. \(-2(3x^2-5)=-(14x^2-298)\)
8. \(-2x^2-50=0\)
9. \(4x^2-676=0\)
10. \(14x^2+477=8x^2-9\)
11. \(2x^2+0=0\)
12. \(-3x^2-1004=-10x^2+4\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(2x^2+8)=-(-16x^2+254) \\ \Leftrightarrow 10x^2+40=16x^2-254 \\ \Leftrightarrow 10x^2-16x^2=-254-40 \\ \Leftrightarrow -6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{-6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(-2(6x^2+3)=-(15x^2+198) \\ \Leftrightarrow -12x^2-6=-15x^2-198 \\ \Leftrightarrow -12x^2+15x^2=-198+6 \\ \Leftrightarrow 3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(15x^2+9=7x^2+9 \\ \Leftrightarrow 15x^2-7x^2=9-9 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(2(5x^2-4)=-(-14x^2+24) \\ \Leftrightarrow 10x^2-8=14x^2-24 \\ \Leftrightarrow 10x^2-14x^2=-24+8 \\ \Leftrightarrow -4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
5. \(-5x^2-7=-8x^2-7 \\ \Leftrightarrow -5x^2+8x^2=-7+7 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-5x^2+30=-8x^2+3 \\ \Leftrightarrow -5x^2+8x^2=3-30 \\ \Leftrightarrow 3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2(3x^2-5)=-(14x^2-298) \\ \Leftrightarrow -6x^2+10=-14x^2+298 \\ \Leftrightarrow -6x^2+14x^2=298-10 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(-2x^2-50=0 \\ \Leftrightarrow -2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{-2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4x^2-676=0 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(14x^2+477=8x^2-9 \\ \Leftrightarrow 14x^2-8x^2=-9-477 \\ \Leftrightarrow 6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2x^2+0=0 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-3x^2-1004=-10x^2+4 \\ \Leftrightarrow -3x^2+10x^2=4+1004 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)