Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(12x^2+1375=5x^2+3\)
2. \(8x^2+968=0\)
3. \(3(2x^2+8)=-(-11x^2-344)\)
4. \(5(-4x^2+3)=-(17x^2+660)\)
5. \(-3(6x^2-8)=-(19x^2-24)\)
6. \(-2(-7x^2-9)=-(-6x^2+54)\)
7. \(-2(-2x^2+6)=-(0x^2-564)\)
8. \(3(7x^2-4)=-(-16x^2+732)\)
9. \(14x^2-850=9x^2-5\)
10. \(4(-6x^2+6)=-(29x^2-24)\)
11. \(x^2-144=0\)
12. \(-11x^2-793=-3x^2+7\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(12x^2+1375=5x^2+3 \\ \Leftrightarrow 12x^2-5x^2=3-1375 \\ \Leftrightarrow 7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{7} < 0 \\ V = \varnothing \\ -----------------\)
2. \(8x^2+968=0 \\ \Leftrightarrow 8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(3(2x^2+8)=-(-11x^2-344) \\ \Leftrightarrow 6x^2+24=11x^2+344 \\ \Leftrightarrow 6x^2-11x^2=344-24 \\ \Leftrightarrow -5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{-5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5(-4x^2+3)=-(17x^2+660) \\ \Leftrightarrow -20x^2+15=-17x^2-660 \\ \Leftrightarrow -20x^2+17x^2=-660-15 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(-3(6x^2-8)=-(19x^2-24) \\ \Leftrightarrow -18x^2+24=-19x^2+24 \\ \Leftrightarrow -18x^2+19x^2=24-24 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-2(-7x^2-9)=-(-6x^2+54) \\ \Leftrightarrow 14x^2+18=6x^2-54 \\ \Leftrightarrow 14x^2-6x^2=-54-18 \\ \Leftrightarrow 8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2(-2x^2+6)=-(0x^2-564) \\ \Leftrightarrow 4x^2-12=0x^2+564 \\ \Leftrightarrow 4x^2+0x^2=564+12 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
8. \(3(7x^2-4)=-(-16x^2+732) \\ \Leftrightarrow 21x^2-12=16x^2-732 \\ \Leftrightarrow 21x^2-16x^2=-732+12 \\ \Leftrightarrow 5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(14x^2-850=9x^2-5 \\ \Leftrightarrow 14x^2-9x^2=-5+850 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(4(-6x^2+6)=-(29x^2-24) \\ \Leftrightarrow -24x^2+24=-29x^2+24 \\ \Leftrightarrow -24x^2+29x^2=24-24 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(x^2-144=0 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
12. \(-11x^2-793=-3x^2+7 \\ \Leftrightarrow -11x^2+3x^2=7+793 \\ \Leftrightarrow -8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{-8} < 0 \\ V = \varnothing \\ -----------------\)