Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-2x^2+8)=-(0x^2-768)\)
2. \(2(-6x^2+8)=-(20x^2+1136)\)
3. \(-9x^2-43=-8x^2-7\)
4. \(5(-7x^2+6)=-(36x^2-174)\)
5. \(x^2-102=-5x^2-6\)
6. \(8x^2+1352=0\)
7. \(7x^2-113=10x^2-5\)
8. \(-x^2-31=5x^2-7\)
9. \(3(4x^2+6)=-(-19x^2+990)\)
10. \(4x^2-58=10x^2-4\)
11. \(-4x^2-676=0\)
12. \(2x^2-18=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-2x^2+8)=-(0x^2-768) \\ \Leftrightarrow 4x^2-16=0x^2+768 \\ \Leftrightarrow 4x^2+0x^2=768+16 \\ \Leftrightarrow 4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(2(-6x^2+8)=-(20x^2+1136) \\ \Leftrightarrow -12x^2+16=-20x^2-1136 \\ \Leftrightarrow -12x^2+20x^2=-1136-16 \\ \Leftrightarrow 8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-9x^2-43=-8x^2-7 \\ \Leftrightarrow -9x^2+8x^2=-7+43 \\ \Leftrightarrow -x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-1} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5(-7x^2+6)=-(36x^2-174) \\ \Leftrightarrow -35x^2+30=-36x^2+174 \\ \Leftrightarrow -35x^2+36x^2=174-30 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
5. \(x^2-102=-5x^2-6 \\ \Leftrightarrow x^2+5x^2=-6+102 \\ \Leftrightarrow 6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(8x^2+1352=0 \\ \Leftrightarrow 8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(7x^2-113=10x^2-5 \\ \Leftrightarrow 7x^2-10x^2=-5+113 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-x^2-31=5x^2-7 \\ \Leftrightarrow -x^2-5x^2=-7+31 \\ \Leftrightarrow -6x^2 = 24 \\ \Leftrightarrow x^2 = \frac{24}{-6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(3(4x^2+6)=-(-19x^2+990) \\ \Leftrightarrow 12x^2+18=19x^2-990 \\ \Leftrightarrow 12x^2-19x^2=-990-18 \\ \Leftrightarrow -7x^2 = -1008 \\ \Leftrightarrow x^2 = \frac{-1008}{-7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
10. \(4x^2-58=10x^2-4 \\ \Leftrightarrow 4x^2-10x^2=-4+58 \\ \Leftrightarrow -6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4x^2-676=0 \\ \Leftrightarrow -4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{-4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2x^2-18=0 \\ \Leftrightarrow 2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)