Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-2x^2-9)=-(13x^2+27)\)
2. \(-3x^2-432=0\)
3. \(7x^2+1183=0\)
4. \(2(10x^2-7)=-(-15x^2-486)\)
5. \(6x^2-1350=0\)
6. \(-x^2+100=0\)
7. \(-6x^2+96=0\)
8. \(5x^2+4=2x^2+7\)
9. \(-7x^2-674=-3x^2+2\)
10. \(3(2x^2-3)=-(-12x^2-1167)\)
11. \(4(-9x^2-5)=-(40x^2-16)\)
12. \(-4(8x^2-6)=-(36x^2+460)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-2x^2-9)=-(13x^2+27) \\ \Leftrightarrow -6x^2-27=-13x^2-27 \\ \Leftrightarrow -6x^2+13x^2=-27+27 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-3x^2-432=0 \\ \Leftrightarrow -3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{-3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(7x^2+1183=0 \\ \Leftrightarrow 7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2(10x^2-7)=-(-15x^2-486) \\ \Leftrightarrow 20x^2-14=15x^2+486 \\ \Leftrightarrow 20x^2-15x^2=486+14 \\ \Leftrightarrow 5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(6x^2-1350=0 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(-x^2+100=0 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(-6x^2+96=0 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(5x^2+4=2x^2+7 \\ \Leftrightarrow 5x^2-2x^2=7-4 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(-7x^2-674=-3x^2+2 \\ \Leftrightarrow -7x^2+3x^2=2+674 \\ \Leftrightarrow -4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(3(2x^2-3)=-(-12x^2-1167) \\ \Leftrightarrow 6x^2-9=12x^2+1167 \\ \Leftrightarrow 6x^2-12x^2=1167+9 \\ \Leftrightarrow -6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(4(-9x^2-5)=-(40x^2-16) \\ \Leftrightarrow -36x^2-20=-40x^2+16 \\ \Leftrightarrow -36x^2+40x^2=16+20 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(-4(8x^2-6)=-(36x^2+460) \\ \Leftrightarrow -32x^2+24=-36x^2-460 \\ \Leftrightarrow -32x^2+36x^2=-460-24 \\ \Leftrightarrow 4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{4} < 0 \\ V = \varnothing \\ -----------------\)