Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2-324=0\)
2. \(11x^2-428=8x^2+4\)
3. \(-x^2+16=0\)
4. \(x^2-49=0\)
5. \(-14x^2-249=-10x^2+7\)
6. \(3(10x^2+8)=-(-37x^2+1159)\)
7. \(5(3x^2+2)=-(-19x^2-14)\)
8. \(-3(-3x^2+6)=-(-7x^2+10)\)
9. \(-4(-2x^2+9)=-(-x^2-412)\)
10. \(5(-5x^2-10)=-(29x^2-526)\)
11. \(3(-2x^2+10)=-(14x^2-678)\)
12. \(-4(-8x^2-4)=-(-39x^2-23)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2-324=0 \\ \Leftrightarrow 4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(11x^2-428=8x^2+4 \\ \Leftrightarrow 11x^2-8x^2=4+428 \\ \Leftrightarrow 3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(-x^2+16=0 \\ \Leftrightarrow -x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(x^2-49=0 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
5. \(-14x^2-249=-10x^2+7 \\ \Leftrightarrow -14x^2+10x^2=7+249 \\ \Leftrightarrow -4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{-4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3(10x^2+8)=-(-37x^2+1159) \\ \Leftrightarrow 30x^2+24=37x^2-1159 \\ \Leftrightarrow 30x^2-37x^2=-1159-24 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(5(3x^2+2)=-(-19x^2-14) \\ \Leftrightarrow 15x^2+10=19x^2+14 \\ \Leftrightarrow 15x^2-19x^2=14-10 \\ \Leftrightarrow -4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{-4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3(-3x^2+6)=-(-7x^2+10) \\ \Leftrightarrow 9x^2-18=7x^2-10 \\ \Leftrightarrow 9x^2-7x^2=-10+18 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
9. \(-4(-2x^2+9)=-(-x^2-412) \\ \Leftrightarrow 8x^2-36=x^2+412 \\ \Leftrightarrow 8x^2-x^2=412+36 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
10. \(5(-5x^2-10)=-(29x^2-526) \\ \Leftrightarrow -25x^2-50=-29x^2+526 \\ \Leftrightarrow -25x^2+29x^2=526+50 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(3(-2x^2+10)=-(14x^2-678) \\ \Leftrightarrow -6x^2+30=-14x^2+678 \\ \Leftrightarrow -6x^2+14x^2=678-30 \\ \Leftrightarrow 8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
12. \(-4(-8x^2-4)=-(-39x^2-23) \\ \Leftrightarrow 32x^2+16=39x^2+23 \\ \Leftrightarrow 32x^2-39x^2=23-16 \\ \Leftrightarrow -7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{-7} < 0 \\ V = \varnothing \\ -----------------\)