Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-7x^2+10)=-(32x^2-184)\)
2. \(-11x^2-9=-4x^2-2\)
3. \(3x^2-190=-5x^2+10\)
4. \(5(2x^2+4)=-(-4x^2-20)\)
5. \(13x^2-150=10x^2-3\)
6. \(4(-3x^2+6)=-(16x^2-40)\)
7. \(-x^2-4=0\)
8. \(8x^2+10=5x^2+7\)
9. \(-4(-5x^2+10)=-(-19x^2+15)\)
10. \(-3x^2+300=0\)
11. \(9x^2+8=5x^2+8\)
12. \(-x^2+36=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-7x^2+10)=-(32x^2-184) \\ \Leftrightarrow -28x^2+40=-32x^2+184 \\ \Leftrightarrow -28x^2+32x^2=184-40 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(-11x^2-9=-4x^2-2 \\ \Leftrightarrow -11x^2+4x^2=-2+9 \\ \Leftrightarrow -7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{-7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(3x^2-190=-5x^2+10 \\ \Leftrightarrow 3x^2+5x^2=10+190 \\ \Leftrightarrow 8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(5(2x^2+4)=-(-4x^2-20) \\ \Leftrightarrow 10x^2+20=4x^2+20 \\ \Leftrightarrow 10x^2-4x^2=20-20 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(13x^2-150=10x^2-3 \\ \Leftrightarrow 13x^2-10x^2=-3+150 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(4(-3x^2+6)=-(16x^2-40) \\ \Leftrightarrow -12x^2+24=-16x^2+40 \\ \Leftrightarrow -12x^2+16x^2=40-24 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
7. \(-x^2-4=0 \\ \Leftrightarrow -x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{-1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(8x^2+10=5x^2+7 \\ \Leftrightarrow 8x^2-5x^2=7-10 \\ \Leftrightarrow 3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-4(-5x^2+10)=-(-19x^2+15) \\ \Leftrightarrow 20x^2-40=19x^2-15 \\ \Leftrightarrow 20x^2-19x^2=-15+40 \\ \Leftrightarrow x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(-3x^2+300=0 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
11. \(9x^2+8=5x^2+8 \\ \Leftrightarrow 9x^2-5x^2=8-8 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-x^2+36=0 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)