Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2+16=0\)
2. \(-11x^2+409=-6x^2+4\)
3. \(-3(3x^2-3)=-(2x^2+166)\)
4. \(-4x^2-45=-7x^2+3\)
5. \(-5(8x^2-5)=-(43x^2-172)\)
6. \(-5x^2-80=0\)
7. \(x^2+2=3x^2-6\)
8. \(-8x^2+392=0\)
9. \(7x^2+47=9x^2-3\)
10. \(10x^2-141=9x^2+3\)
11. \(7x^2+0=0\)
12. \(5(-4x^2-3)=-(15x^2+335)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2+16=0 \\ \Leftrightarrow -x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-11x^2+409=-6x^2+4 \\ \Leftrightarrow -11x^2+6x^2=4-409 \\ \Leftrightarrow -5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{-5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
3. \(-3(3x^2-3)=-(2x^2+166) \\ \Leftrightarrow -9x^2+9=-2x^2-166 \\ \Leftrightarrow -9x^2+2x^2=-166-9 \\ \Leftrightarrow -7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{-7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(-4x^2-45=-7x^2+3 \\ \Leftrightarrow -4x^2+7x^2=3+45 \\ \Leftrightarrow 3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
5. \(-5(8x^2-5)=-(43x^2-172) \\ \Leftrightarrow -40x^2+25=-43x^2+172 \\ \Leftrightarrow -40x^2+43x^2=172-25 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(-5x^2-80=0 \\ \Leftrightarrow -5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{-5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(x^2+2=3x^2-6 \\ \Leftrightarrow x^2-3x^2=-6-2 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(-8x^2+392=0 \\ \Leftrightarrow -8x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{-8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(7x^2+47=9x^2-3 \\ \Leftrightarrow 7x^2-9x^2=-3-47 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(10x^2-141=9x^2+3 \\ \Leftrightarrow 10x^2-9x^2=3+141 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(7x^2+0=0 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(5(-4x^2-3)=-(15x^2+335) \\ \Leftrightarrow -20x^2-15=-15x^2-335 \\ \Leftrightarrow -20x^2+15x^2=-335+15 \\ \Leftrightarrow -5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{-5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)