Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2-203=9x^2-3\)
2. \(4(-6x^2+2)=-(31x^2-1380)\)
3. \(-6x^2-135=-8x^2-7\)
4. \(10x^2-141=6x^2+3\)
5. \(5x^2-4=3x^2-4\)
6. \(5x^2-27=-3x^2+5\)
7. \(5(-8x^2+9)=-(46x^2-1395)\)
8. \(-2x^2-392=0\)
9. \(-x^2+81=0\)
10. \(-6x^2+1350=0\)
11. \(2x^2-259=6x^2-3\)
12. \(-4(5x^2+4)=-(18x^2+16)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2-203=9x^2-3 \\ \Leftrightarrow 7x^2-9x^2=-3+203 \\ \Leftrightarrow -2x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(4(-6x^2+2)=-(31x^2-1380) \\ \Leftrightarrow -24x^2+8=-31x^2+1380 \\ \Leftrightarrow -24x^2+31x^2=1380-8 \\ \Leftrightarrow 7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-6x^2-135=-8x^2-7 \\ \Leftrightarrow -6x^2+8x^2=-7+135 \\ \Leftrightarrow 2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(10x^2-141=6x^2+3 \\ \Leftrightarrow 10x^2-6x^2=3+141 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
5. \(5x^2-4=3x^2-4 \\ \Leftrightarrow 5x^2-3x^2=-4+4 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(5x^2-27=-3x^2+5 \\ \Leftrightarrow 5x^2+3x^2=5+27 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
7. \(5(-8x^2+9)=-(46x^2-1395) \\ \Leftrightarrow -40x^2+45=-46x^2+1395 \\ \Leftrightarrow -40x^2+46x^2=1395-45 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(-2x^2-392=0 \\ \Leftrightarrow -2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-x^2+81=0 \\ \Leftrightarrow -x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{-1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-6x^2+1350=0 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(2x^2-259=6x^2-3 \\ \Leftrightarrow 2x^2-6x^2=-3+259 \\ \Leftrightarrow -4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{-4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-4(5x^2+4)=-(18x^2+16) \\ \Leftrightarrow -20x^2-16=-18x^2-16 \\ \Leftrightarrow -20x^2+18x^2=-16+16 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)