Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+138=7x^2-9\)
2. \(-2(-8x^2+6)=-(-20x^2+12)\)
3. \(-8x^2-968=0\)
4. \(2x^2+32=0\)
5. \(-4(6x^2-8)=-(32x^2+168)\)
6. \(2(3x^2+6)=-(-5x^2-12)\)
7. \(13x^2+181=6x^2+6\)
8. \(6x^2-600=0\)
9. \(-4(-5x^2-9)=-(-24x^2+64)\)
10. \(8x^2-392=0\)
11. \(4(4x^2+3)=-(-23x^2-187)\)
12. \(5x^2-125=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+138=7x^2-9 \\ \Leftrightarrow 4x^2-7x^2=-9-138 \\ \Leftrightarrow -3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{-3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(-2(-8x^2+6)=-(-20x^2+12) \\ \Leftrightarrow 16x^2-12=20x^2-12 \\ \Leftrightarrow 16x^2-20x^2=-12+12 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-8x^2-968=0 \\ \Leftrightarrow -8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{-8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2x^2+32=0 \\ \Leftrightarrow 2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-4(6x^2-8)=-(32x^2+168) \\ \Leftrightarrow -24x^2+32=-32x^2-168 \\ \Leftrightarrow -24x^2+32x^2=-168-32 \\ \Leftrightarrow 8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(2(3x^2+6)=-(-5x^2-12) \\ \Leftrightarrow 6x^2+12=5x^2+12 \\ \Leftrightarrow 6x^2-5x^2=12-12 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(13x^2+181=6x^2+6 \\ \Leftrightarrow 13x^2-6x^2=6-181 \\ \Leftrightarrow 7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(6x^2-600=0 \\ \Leftrightarrow 6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-4(-5x^2-9)=-(-24x^2+64) \\ \Leftrightarrow 20x^2+36=24x^2-64 \\ \Leftrightarrow 20x^2-24x^2=-64-36 \\ \Leftrightarrow -4x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(8x^2-392=0 \\ \Leftrightarrow 8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(4(4x^2+3)=-(-23x^2-187) \\ \Leftrightarrow 16x^2+12=23x^2+187 \\ \Leftrightarrow 16x^2-23x^2=187-12 \\ \Leftrightarrow -7x^2 = 175 \\ \Leftrightarrow x^2 = \frac{175}{-7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(5x^2-125=0 \\ \Leftrightarrow 5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)