Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2-2=0\)
2. \(3(4x^2-6)=-(-11x^2+18)\)
3. \(-2x^2+242=0\)
4. \(4(8x^2-3)=-(-38x^2+12)\)
5. \(x^2-6=-3x^2-6\)
6. \(6x^2+0=0\)
7. \(4x^2-144=0\)
8. \(3(-4x^2-4)=-(19x^2+12)\)
9. \(-3(-9x^2-7)=-(-32x^2-426)\)
10. \(4x^2+146=8x^2+2\)
11. \(5(4x^2+9)=-(-14x^2-261)\)
12. \(-3x^2-723=3x^2+3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2-2=0 \\ \Leftrightarrow -2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(3(4x^2-6)=-(-11x^2+18) \\ \Leftrightarrow 12x^2-18=11x^2-18 \\ \Leftrightarrow 12x^2-11x^2=-18+18 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-2x^2+242=0 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(4(8x^2-3)=-(-38x^2+12) \\ \Leftrightarrow 32x^2-12=38x^2-12 \\ \Leftrightarrow 32x^2-38x^2=-12+12 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(x^2-6=-3x^2-6 \\ \Leftrightarrow x^2+3x^2=-6+6 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(4x^2-144=0 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(3(-4x^2-4)=-(19x^2+12) \\ \Leftrightarrow -12x^2-12=-19x^2-12 \\ \Leftrightarrow -12x^2+19x^2=-12+12 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-3(-9x^2-7)=-(-32x^2-426) \\ \Leftrightarrow 27x^2+21=32x^2+426 \\ \Leftrightarrow 27x^2-32x^2=426-21 \\ \Leftrightarrow -5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{-5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(4x^2+146=8x^2+2 \\ \Leftrightarrow 4x^2-8x^2=2-146 \\ \Leftrightarrow -4x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{-4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(5(4x^2+9)=-(-14x^2-261) \\ \Leftrightarrow 20x^2+45=14x^2+261 \\ \Leftrightarrow 20x^2-14x^2=261-45 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(-3x^2-723=3x^2+3 \\ \Leftrightarrow -3x^2-3x^2=3+723 \\ \Leftrightarrow -6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{-6} < 0 \\ V = \varnothing \\ -----------------\)