Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2-12=5x^2-9\)
2. \(-3x^2-75=0\)
3. \(-6x^2+36=2x^2+4\)
4. \(10x^2-33=9x^2-8\)
5. \(4x^2+140=10x^2-10\)
6. \(6x^2-6=0\)
7. \(-2(-7x^2+3)=-(-15x^2-43)\)
8. \(x^2-4=0\)
9. \(-5x^2+125=0\)
10. \(-2(6x^2+8)=-(17x^2-29)\)
11. \(5x^2+3=-2x^2+3\)
12. \(-2(-8x^2+2)=-(-10x^2-20)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2-12=5x^2-9 \\ \Leftrightarrow 8x^2-5x^2=-9+12 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
2. \(-3x^2-75=0 \\ \Leftrightarrow -3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{-3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-6x^2+36=2x^2+4 \\ \Leftrightarrow -6x^2-2x^2=4-36 \\ \Leftrightarrow -8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
4. \(10x^2-33=9x^2-8 \\ \Leftrightarrow 10x^2-9x^2=-8+33 \\ \Leftrightarrow x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(4x^2+140=10x^2-10 \\ \Leftrightarrow 4x^2-10x^2=-10-140 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(6x^2-6=0 \\ \Leftrightarrow 6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(-2(-7x^2+3)=-(-15x^2-43) \\ \Leftrightarrow 14x^2-6=15x^2+43 \\ \Leftrightarrow 14x^2-15x^2=43+6 \\ \Leftrightarrow -x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{-1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(x^2-4=0 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
9. \(-5x^2+125=0 \\ \Leftrightarrow -5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{-5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(-2(6x^2+8)=-(17x^2-29) \\ \Leftrightarrow -12x^2-16=-17x^2+29 \\ \Leftrightarrow -12x^2+17x^2=29+16 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(5x^2+3=-2x^2+3 \\ \Leftrightarrow 5x^2+2x^2=3-3 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-2(-8x^2+2)=-(-10x^2-20) \\ \Leftrightarrow 16x^2-4=10x^2+20 \\ \Leftrightarrow 16x^2-10x^2=20+4 \\ \Leftrightarrow 6x^2 = 24 \\ \Leftrightarrow x^2 = \frac{24}{6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)