Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2+31=6x^2-5\)
2. \(2(9x^2-4)=-(-12x^2-856)\)
3. \(3x^2+0=0\)
4. \(5(-10x^2-6)=-(53x^2+78)\)
5. \(11x^2-578=8x^2+10\)
6. \(-4x^2-16=0\)
7. \(-6x^2-150=0\)
8. \(5(9x^2+7)=-(-40x^2-40)\)
9. \(-3x^2+300=0\)
10. \(3x^2-105=2x^2-5\)
11. \(6x^2-96=0\)
12. \(2x^2-392=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2+31=6x^2-5 \\ \Leftrightarrow 2x^2-6x^2=-5-31 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
2. \(2(9x^2-4)=-(-12x^2-856) \\ \Leftrightarrow 18x^2-8=12x^2+856 \\ \Leftrightarrow 18x^2-12x^2=856+8 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(3x^2+0=0 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(5(-10x^2-6)=-(53x^2+78) \\ \Leftrightarrow -50x^2-30=-53x^2-78 \\ \Leftrightarrow -50x^2+53x^2=-78+30 \\ \Leftrightarrow 3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(11x^2-578=8x^2+10 \\ \Leftrightarrow 11x^2-8x^2=10+578 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(-4x^2-16=0 \\ \Leftrightarrow -4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-4} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-6x^2-150=0 \\ \Leftrightarrow -6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{-6} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5(9x^2+7)=-(-40x^2-40) \\ \Leftrightarrow 45x^2+35=40x^2+40 \\ \Leftrightarrow 45x^2-40x^2=40-35 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-3x^2+300=0 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
10. \(3x^2-105=2x^2-5 \\ \Leftrightarrow 3x^2-2x^2=-5+105 \\ \Leftrightarrow x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
11. \(6x^2-96=0 \\ \Leftrightarrow 6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(2x^2-392=0 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)