Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2+1184=9x^2+8\)
2. \(-3(-4x^2-7)=-(-11x^2+28)\)
3. \(-3x^2+675=0\)
4. \(-5(-9x^2+5)=-(-48x^2-650)\)
5. \(-2x^2-668=-6x^2+8\)
6. \(-5(4x^2-3)=-(13x^2+48)\)
7. \(7x^2-343=0\)
8. \(7x^2-1372=0\)
9. \(5(-8x^2-5)=-(35x^2+430)\)
10. \(-5(-5x^2-4)=-(-24x^2-141)\)
11. \(-2x^2-855=-7x^2-10\)
12. \(3(5x^2+8)=-(-23x^2-24)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2+1184=9x^2+8 \\ \Leftrightarrow 3x^2-9x^2=8-1184 \\ \Leftrightarrow -6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(-3(-4x^2-7)=-(-11x^2+28) \\ \Leftrightarrow 12x^2+21=11x^2-28 \\ \Leftrightarrow 12x^2-11x^2=-28-21 \\ \Leftrightarrow x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-3x^2+675=0 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(-5(-9x^2+5)=-(-48x^2-650) \\ \Leftrightarrow 45x^2-25=48x^2+650 \\ \Leftrightarrow 45x^2-48x^2=650+25 \\ \Leftrightarrow -3x^2 = 675 \\ \Leftrightarrow x^2 = \frac{675}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-2x^2-668=-6x^2+8 \\ \Leftrightarrow -2x^2+6x^2=8+668 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(-5(4x^2-3)=-(13x^2+48) \\ \Leftrightarrow -20x^2+15=-13x^2-48 \\ \Leftrightarrow -20x^2+13x^2=-48-15 \\ \Leftrightarrow -7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{-7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(7x^2-343=0 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(7x^2-1372=0 \\ \Leftrightarrow 7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(5(-8x^2-5)=-(35x^2+430) \\ \Leftrightarrow -40x^2-25=-35x^2-430 \\ \Leftrightarrow -40x^2+35x^2=-430+25 \\ \Leftrightarrow -5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{-5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-5(-5x^2-4)=-(-24x^2-141) \\ \Leftrightarrow 25x^2+20=24x^2+141 \\ \Leftrightarrow 25x^2-24x^2=141-20 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-2x^2-855=-7x^2-10 \\ \Leftrightarrow -2x^2+7x^2=-10+855 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(3(5x^2+8)=-(-23x^2-24) \\ \Leftrightarrow 15x^2+24=23x^2+24 \\ \Leftrightarrow 15x^2-23x^2=24-24 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)