Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+242=0\)
2. \(-6x^2-395=-10x^2+5\)
3. \(-5x^2-134=-9x^2+10\)
4. \(-2(3x^2+3)=-(x^2-714)\)
5. \(-11x^2+62=-3x^2-10\)
6. \(-6x^2+54=0\)
7. \(-2(-10x^2-6)=-(-28x^2+500)\)
8. \(-4x^2+576=0\)
9. \(-x^2-25=0\)
10. \(-5(3x^2+9)=-(13x^2-53)\)
11. \(5x^2-845=0\)
12. \(x^2+573=8x^2+6\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+242=0 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(-6x^2-395=-10x^2+5 \\ \Leftrightarrow -6x^2+10x^2=5+395 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(-5x^2-134=-9x^2+10 \\ \Leftrightarrow -5x^2+9x^2=10+134 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(-2(3x^2+3)=-(x^2-714) \\ \Leftrightarrow -6x^2-6=-x^2+714 \\ \Leftrightarrow -6x^2+x^2=714+6 \\ \Leftrightarrow -5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{-5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-11x^2+62=-3x^2-10 \\ \Leftrightarrow -11x^2+3x^2=-10-62 \\ \Leftrightarrow -8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(-6x^2+54=0 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(-2(-10x^2-6)=-(-28x^2+500) \\ \Leftrightarrow 20x^2+12=28x^2-500 \\ \Leftrightarrow 20x^2-28x^2=-500-12 \\ \Leftrightarrow -8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{-8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-4x^2+576=0 \\ \Leftrightarrow -4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{-4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
9. \(-x^2-25=0 \\ \Leftrightarrow -x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{-1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-5(3x^2+9)=-(13x^2-53) \\ \Leftrightarrow -15x^2-45=-13x^2+53 \\ \Leftrightarrow -15x^2+13x^2=53+45 \\ \Leftrightarrow -2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{-2} < 0 \\ V = \varnothing \\ -----------------\)
11. \(5x^2-845=0 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(x^2+573=8x^2+6 \\ \Leftrightarrow x^2-8x^2=6-573 \\ \Leftrightarrow -7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{-7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)