Onvolledige VKV (b=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-648=0\)
2. \(-8x^2+800=0\)
3. \(-8x^2+0=0\)
4. \(-2(-9x^2+3)=-(-14x^2-478)\)
5. \(2x^2+18=5x^2+6\)
6. \(-2x^2+450=0\)
7. \(-4(9x^2+5)=-(29x^2+1392)\)
8. \(3(8x^2-10)=-(-19x^2-470)\)
9. \(-2(-5x^2+10)=-(-16x^2+20)\)
10. \(8x^2+1152=0\)
11. \(2x^2-200=0\)
12. \(-3(-5x^2-8)=-(-12x^2+168)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-648=0 \\ \Leftrightarrow -8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{-8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-8x^2+800=0 \\ \Leftrightarrow -8x^2 = -800 \\ \Leftrightarrow x^2 = \frac{-800}{-8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-2(-9x^2+3)=-(-14x^2-478) \\ \Leftrightarrow 18x^2-6=14x^2+478 \\ \Leftrightarrow 18x^2-14x^2=478+6 \\ \Leftrightarrow 4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(2x^2+18=5x^2+6 \\ \Leftrightarrow 2x^2-5x^2=6-18 \\ \Leftrightarrow -3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{-3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(-2x^2+450=0 \\ \Leftrightarrow -2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{-2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(-4(9x^2+5)=-(29x^2+1392) \\ \Leftrightarrow -36x^2-20=-29x^2-1392 \\ \Leftrightarrow -36x^2+29x^2=-1392+20 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(3(8x^2-10)=-(-19x^2-470) \\ \Leftrightarrow 24x^2-30=19x^2+470 \\ \Leftrightarrow 24x^2-19x^2=470+30 \\ \Leftrightarrow 5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-2(-5x^2+10)=-(-16x^2+20) \\ \Leftrightarrow 10x^2-20=16x^2-20 \\ \Leftrightarrow 10x^2-16x^2=-20+20 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(8x^2+1152=0 \\ \Leftrightarrow 8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2x^2-200=0 \\ \Leftrightarrow 2x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{2}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(-3(-5x^2-8)=-(-12x^2+168) \\ \Leftrightarrow 15x^2+24=12x^2-168 \\ \Leftrightarrow 15x^2-12x^2=-168-24 \\ \Leftrightarrow 3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{3} < 0 \\ V = \varnothing \\ -----------------\)