Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(11x^2+4=3x^2+4\)
2. \(-3(5x^2+8)=-(9x^2+24)\)
3. \(4(6x^2+3)=-(-29x^2-12)\)
4. \(-4(5x^2+4)=-(12x^2+216)\)
5. \(-5x^2-405=0\)
6. \(6x^2-486=0\)
7. \(-17x^2+515=-9x^2+3\)
8. \(-5x^2-1125=0\)
9. \(10x^2+147=4x^2-3\)
10. \(-2(9x^2+3)=-(24x^2+12)\)
11. \(14x^2+7=8x^2+7\)
12. \(3(-4x^2+2)=-(5x^2+442)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(11x^2+4=3x^2+4 \\ \Leftrightarrow 11x^2-3x^2=4-4 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-3(5x^2+8)=-(9x^2+24) \\ \Leftrightarrow -15x^2-24=-9x^2-24 \\ \Leftrightarrow -15x^2+9x^2=-24+24 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(4(6x^2+3)=-(-29x^2-12) \\ \Leftrightarrow 24x^2+12=29x^2+12 \\ \Leftrightarrow 24x^2-29x^2=12-12 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-4(5x^2+4)=-(12x^2+216) \\ \Leftrightarrow -20x^2-16=-12x^2-216 \\ \Leftrightarrow -20x^2+12x^2=-216+16 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-5x^2-405=0 \\ \Leftrightarrow -5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(6x^2-486=0 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(-17x^2+515=-9x^2+3 \\ \Leftrightarrow -17x^2+9x^2=3-515 \\ \Leftrightarrow -8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{-8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-5x^2-1125=0 \\ \Leftrightarrow -5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{-5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(10x^2+147=4x^2-3 \\ \Leftrightarrow 10x^2-4x^2=-3-147 \\ \Leftrightarrow 6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2(9x^2+3)=-(24x^2+12) \\ \Leftrightarrow -18x^2-6=-24x^2-12 \\ \Leftrightarrow -18x^2+24x^2=-12+6 \\ \Leftrightarrow 6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(14x^2+7=8x^2+7 \\ \Leftrightarrow 14x^2-8x^2=7-7 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(3(-4x^2+2)=-(5x^2+442) \\ \Leftrightarrow -12x^2+6=-5x^2-442 \\ \Leftrightarrow -12x^2+5x^2=-442-6 \\ \Leftrightarrow -7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{-7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)