Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(9x^2+7)=-(17x^2+14)\)
2. \(-5(5x^2-3)=-(23x^2-143)\)
3. \(-8x^2+0=0\)
4. \(7x^2-448=0\)
5. \(-3(-6x^2+10)=-(-19x^2+111)\)
6. \(-5(8x^2-6)=-(35x^2+470)\)
7. \(15x^2+600=10x^2-5\)
8. \(-5x^2+8=-2x^2+5\)
9. \(5x^2+720=0\)
10. \(5x^2+405=0\)
11. \(-5(-10x^2-5)=-(-46x^2-601)\)
12. \(-2x^2-18=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(9x^2+7)=-(17x^2+14) \\ \Leftrightarrow -18x^2-14=-17x^2-14 \\ \Leftrightarrow -18x^2+17x^2=-14+14 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-5(5x^2-3)=-(23x^2-143) \\ \Leftrightarrow -25x^2+15=-23x^2+143 \\ \Leftrightarrow -25x^2+23x^2=143-15 \\ \Leftrightarrow -2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(7x^2-448=0 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(-3(-6x^2+10)=-(-19x^2+111) \\ \Leftrightarrow 18x^2-30=19x^2-111 \\ \Leftrightarrow 18x^2-19x^2=-111+30 \\ \Leftrightarrow -x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{-1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-5(8x^2-6)=-(35x^2+470) \\ \Leftrightarrow -40x^2+30=-35x^2-470 \\ \Leftrightarrow -40x^2+35x^2=-470-30 \\ \Leftrightarrow -5x^2 = -500 \\ \Leftrightarrow x^2 = \frac{-500}{-5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(15x^2+600=10x^2-5 \\ \Leftrightarrow 15x^2-10x^2=-5-600 \\ \Leftrightarrow 5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5x^2+8=-2x^2+5 \\ \Leftrightarrow -5x^2+2x^2=5-8 \\ \Leftrightarrow -3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{-3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(5x^2+720=0 \\ \Leftrightarrow 5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(5x^2+405=0 \\ \Leftrightarrow 5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-5(-10x^2-5)=-(-46x^2-601) \\ \Leftrightarrow 50x^2+25=46x^2+601 \\ \Leftrightarrow 50x^2-46x^2=601-25 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
12. \(-2x^2-18=0 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)