Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2-3=6x^2-3\)
2. \(12x^2+58=10x^2+8\)
3. \(-6x^2+56=-5x^2-8\)
4. \(-8x^2-414=-3x^2-9\)
5. \(7x^2-448=0\)
6. \(3(8x^2-10)=-(-20x^2-226)\)
7. \(-4(9x^2-2)=-(37x^2-72)\)
8. \(-4(3x^2+4)=-(10x^2-322)\)
9. \(-8x^2+648=0\)
10. \(-12x^2-6=-4x^2+2\)
11. \(-3(-2x^2+10)=-(0x^2+30)\)
12. \(8x^2-1152=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2-3=6x^2-3 \\ \Leftrightarrow -2x^2-6x^2=-3+3 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(12x^2+58=10x^2+8 \\ \Leftrightarrow 12x^2-10x^2=8-58 \\ \Leftrightarrow 2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-6x^2+56=-5x^2-8 \\ \Leftrightarrow -6x^2+5x^2=-8-56 \\ \Leftrightarrow -x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-8x^2-414=-3x^2-9 \\ \Leftrightarrow -8x^2+3x^2=-9+414 \\ \Leftrightarrow -5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{-5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(7x^2-448=0 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
6. \(3(8x^2-10)=-(-20x^2-226) \\ \Leftrightarrow 24x^2-30=20x^2+226 \\ \Leftrightarrow 24x^2-20x^2=226+30 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(-4(9x^2-2)=-(37x^2-72) \\ \Leftrightarrow -36x^2+8=-37x^2+72 \\ \Leftrightarrow -36x^2+37x^2=72-8 \\ \Leftrightarrow x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-4(3x^2+4)=-(10x^2-322) \\ \Leftrightarrow -12x^2-16=-10x^2+322 \\ \Leftrightarrow -12x^2+10x^2=322+16 \\ \Leftrightarrow -2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{-2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-8x^2+648=0 \\ \Leftrightarrow -8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{-8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-12x^2-6=-4x^2+2 \\ \Leftrightarrow -12x^2+4x^2=2+6 \\ \Leftrightarrow -8x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{-8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-3(-2x^2+10)=-(0x^2+30) \\ \Leftrightarrow 6x^2-30=0x^2-30 \\ \Leftrightarrow 6x^2+0x^2=-30+30 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(8x^2-1152=0 \\ \Leftrightarrow 8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)