Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2-1014=0\)
2. \(-10x^2+11=-6x^2+7\)
3. \(-5(3x^2-3)=-(14x^2+154)\)
4. \(5x^2-845=0\)
5. \(-4x^2+22=-7x^2-5\)
6. \(7x^2-1008=0\)
7. \(-7x^2+0=0\)
8. \(4x^2-36=0\)
9. \(-4x^2-484=0\)
10. \(2x^2+4=10x^2+4\)
11. \(11x^2-10=10x^2-9\)
12. \(-3x^2-588=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2-1014=0 \\ \Leftrightarrow 6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
2. \(-10x^2+11=-6x^2+7 \\ \Leftrightarrow -10x^2+6x^2=7-11 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(-5(3x^2-3)=-(14x^2+154) \\ \Leftrightarrow -15x^2+15=-14x^2-154 \\ \Leftrightarrow -15x^2+14x^2=-154-15 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(5x^2-845=0 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
5. \(-4x^2+22=-7x^2-5 \\ \Leftrightarrow -4x^2+7x^2=-5-22 \\ \Leftrightarrow 3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{3} < 0 \\ V = \varnothing \\ -----------------\)
6. \(7x^2-1008=0 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
7. \(-7x^2+0=0 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(4x^2-36=0 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-4x^2-484=0 \\ \Leftrightarrow -4x^2 = 484 \\ \Leftrightarrow x^2 = \frac{484}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(2x^2+4=10x^2+4 \\ \Leftrightarrow 2x^2-10x^2=4-4 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(11x^2-10=10x^2-9 \\ \Leftrightarrow 11x^2-10x^2=-9+10 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
12. \(-3x^2-588=0 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)