Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(4x^2-2)=-(-11x^2+2)\)
2. \(3(3x^2-5)=-(-x^2-57)\)
3. \(4x^2-36=0\)
4. \(-3x^2+12=0\)
5. \(8x^2-1800=0\)
6. \(-3x^2-43=-5x^2+7\)
7. \(3(-10x^2+3)=-(24x^2+45)\)
8. \(-2(7x^2-3)=-(8x^2+480)\)
9. \(8x^2+8=0\)
10. \(5(-10x^2+10)=-(49x^2-46)\)
11. \(4(-8x^2+9)=-(36x^2-292)\)
12. \(-2(-7x^2-9)=-(-12x^2-26)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(4x^2-2)=-(-11x^2+2) \\ \Leftrightarrow 12x^2-6=11x^2-2 \\ \Leftrightarrow 12x^2-11x^2=-2+6 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(3(3x^2-5)=-(-x^2-57) \\ \Leftrightarrow 9x^2-15=x^2+57 \\ \Leftrightarrow 9x^2-x^2=57+15 \\ \Leftrightarrow 8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(4x^2-36=0 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(-3x^2+12=0 \\ \Leftrightarrow -3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{-3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
5. \(8x^2-1800=0 \\ \Leftrightarrow 8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(-3x^2-43=-5x^2+7 \\ \Leftrightarrow -3x^2+5x^2=7+43 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(3(-10x^2+3)=-(24x^2+45) \\ \Leftrightarrow -30x^2+9=-24x^2-45 \\ \Leftrightarrow -30x^2+24x^2=-45-9 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
8. \(-2(7x^2-3)=-(8x^2+480) \\ \Leftrightarrow -14x^2+6=-8x^2-480 \\ \Leftrightarrow -14x^2+8x^2=-480-6 \\ \Leftrightarrow -6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{-6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(8x^2+8=0 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(5(-10x^2+10)=-(49x^2-46) \\ \Leftrightarrow -50x^2+50=-49x^2+46 \\ \Leftrightarrow -50x^2+49x^2=46-50 \\ \Leftrightarrow -x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
11. \(4(-8x^2+9)=-(36x^2-292) \\ \Leftrightarrow -32x^2+36=-36x^2+292 \\ \Leftrightarrow -32x^2+36x^2=292-36 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(-2(-7x^2-9)=-(-12x^2-26) \\ \Leftrightarrow 14x^2+18=12x^2+26 \\ \Leftrightarrow 14x^2-12x^2=26-18 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)