Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2+80=0\)
2. \(4(7x^2+9)=-(-20x^2-68)\)
3. \(4x^2+576=0\)
4. \(-4x^2+900=0\)
5. \(-4x^2-784=0\)
6. \(-4(3x^2+7)=-(17x^2-952)\)
7. \(5x^2-180=0\)
8. \(-8x^2+648=0\)
9. \(5x^2-9=3x^2+9\)
10. \(-6x^2-1014=0\)
11. \(-4x^2+3=-10x^2+3\)
12. \(2x^2+1=6x^2-3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2+80=0 \\ \Leftrightarrow 5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{5} < 0 \\ V = \varnothing \\ -----------------\)
2. \(4(7x^2+9)=-(-20x^2-68) \\ \Leftrightarrow 28x^2+36=20x^2+68 \\ \Leftrightarrow 28x^2-20x^2=68-36 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(4x^2+576=0 \\ \Leftrightarrow 4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-4x^2+900=0 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(-4x^2-784=0 \\ \Leftrightarrow -4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{-4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4(3x^2+7)=-(17x^2-952) \\ \Leftrightarrow -12x^2-28=-17x^2+952 \\ \Leftrightarrow -12x^2+17x^2=952+28 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(5x^2-180=0 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(-8x^2+648=0 \\ \Leftrightarrow -8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{-8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(5x^2-9=3x^2+9 \\ \Leftrightarrow 5x^2-3x^2=9+9 \\ \Leftrightarrow 2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(-6x^2-1014=0 \\ \Leftrightarrow -6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4x^2+3=-10x^2+3 \\ \Leftrightarrow -4x^2+10x^2=3-3 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(2x^2+1=6x^2-3 \\ \Leftrightarrow 2x^2-6x^2=-3-1 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)