Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+0=0\)
2. \(4(-9x^2+6)=-(29x^2-472)\)
3. \(-3x^2-108=0\)
4. \(5x^2+980=0\)
5. \(-4x^2+4=0\)
6. \(x^2+40=2x^2+4\)
7. \(3x^2-51=-2x^2-6\)
8. \(-x^2-225=0\)
9. \(2x^2+0=0\)
10. \(-5(-3x^2-2)=-(-11x^2-686)\)
11. \(-5(-4x^2+5)=-(-23x^2+217)\)
12. \(-3(-7x^2+5)=-(-20x^2+24)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+0=0 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(4(-9x^2+6)=-(29x^2-472) \\ \Leftrightarrow -36x^2+24=-29x^2+472 \\ \Leftrightarrow -36x^2+29x^2=472-24 \\ \Leftrightarrow -7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{-7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-3x^2-108=0 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5x^2+980=0 \\ \Leftrightarrow 5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-4x^2+4=0 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(x^2+40=2x^2+4 \\ \Leftrightarrow x^2-2x^2=4-40 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(3x^2-51=-2x^2-6 \\ \Leftrightarrow 3x^2+2x^2=-6+51 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
8. \(-x^2-225=0 \\ \Leftrightarrow -x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{-1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(2x^2+0=0 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-5(-3x^2-2)=-(-11x^2-686) \\ \Leftrightarrow 15x^2+10=11x^2+686 \\ \Leftrightarrow 15x^2-11x^2=686-10 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(-5(-4x^2+5)=-(-23x^2+217) \\ \Leftrightarrow 20x^2-25=23x^2-217 \\ \Leftrightarrow 20x^2-23x^2=-217+25 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(-3(-7x^2+5)=-(-20x^2+24) \\ \Leftrightarrow 21x^2-15=20x^2-24 \\ \Leftrightarrow 21x^2-20x^2=-24+15 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)