Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(8x^2-9)=-(23x^2-466)\)
2. \(-5(4x^2+5)=-(26x^2-989)\)
3. \(14x^2+4=6x^2+4\)
4. \(-3x^2+0=0\)
5. \(3(-8x^2+5)=-(19x^2-515)\)
6. \(-3(6x^2-9)=-(15x^2+48)\)
7. \(-2(-7x^2+7)=-(-20x^2+14)\)
8. \(-4(-7x^2-5)=-(-33x^2+825)\)
9. \(-8x^2+800=0\)
10. \(7x^2+448=0\)
11. \(15x^2-10=8x^2-10\)
12. \(-3x^2+260=-10x^2+8\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(8x^2-9)=-(23x^2-466) \\ \Leftrightarrow -16x^2+18=-23x^2+466 \\ \Leftrightarrow -16x^2+23x^2=466-18 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
2. \(-5(4x^2+5)=-(26x^2-989) \\ \Leftrightarrow -20x^2-25=-26x^2+989 \\ \Leftrightarrow -20x^2+26x^2=989+25 \\ \Leftrightarrow 6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(14x^2+4=6x^2+4 \\ \Leftrightarrow 14x^2-6x^2=4-4 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-3x^2+0=0 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(3(-8x^2+5)=-(19x^2-515) \\ \Leftrightarrow -24x^2+15=-19x^2+515 \\ \Leftrightarrow -24x^2+19x^2=515-15 \\ \Leftrightarrow -5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-3(6x^2-9)=-(15x^2+48) \\ \Leftrightarrow -18x^2+27=-15x^2-48 \\ \Leftrightarrow -18x^2+15x^2=-48-27 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
7. \(-2(-7x^2+7)=-(-20x^2+14) \\ \Leftrightarrow 14x^2-14=20x^2-14 \\ \Leftrightarrow 14x^2-20x^2=-14+14 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-4(-7x^2-5)=-(-33x^2+825) \\ \Leftrightarrow 28x^2+20=33x^2-825 \\ \Leftrightarrow 28x^2-33x^2=-825-20 \\ \Leftrightarrow -5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{-5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-8x^2+800=0 \\ \Leftrightarrow -8x^2 = -800 \\ \Leftrightarrow x^2 = \frac{-800}{-8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
10. \(7x^2+448=0 \\ \Leftrightarrow 7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(15x^2-10=8x^2-10 \\ \Leftrightarrow 15x^2-8x^2=-10+10 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-3x^2+260=-10x^2+8 \\ \Leftrightarrow -3x^2+10x^2=8-260 \\ \Leftrightarrow 7x^2 = -252 \\ \Leftrightarrow x^2 = \frac{-252}{7} < 0 \\ V = \varnothing \\ -----------------\)