Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2-105=-2x^2-9\)
2. \(4x^2+7=9x^2+7\)
3. \(-2x^2+6=-9x^2+6\)
4. \(-2(8x^2-4)=-(11x^2+12)\)
5. \(2(-7x^2+6)=-(12x^2-10)\)
6. \(4x^2+0=0\)
7. \(-3x^2+9=4x^2+2\)
8. \(-5x^2+605=0\)
9. \(-7x^2+33=-8x^2-3\)
10. \(4(-4x^2-7)=-(8x^2+1596)\)
11. \(3x^2-588=0\)
12. \(-7x^2+112=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2-105=-2x^2-9 \\ \Leftrightarrow 4x^2+2x^2=-9+105 \\ \Leftrightarrow 6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(4x^2+7=9x^2+7 \\ \Leftrightarrow 4x^2-9x^2=7-7 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-2x^2+6=-9x^2+6 \\ \Leftrightarrow -2x^2+9x^2=6-6 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-2(8x^2-4)=-(11x^2+12) \\ \Leftrightarrow -16x^2+8=-11x^2-12 \\ \Leftrightarrow -16x^2+11x^2=-12-8 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
5. \(2(-7x^2+6)=-(12x^2-10) \\ \Leftrightarrow -14x^2+12=-12x^2+10 \\ \Leftrightarrow -14x^2+12x^2=10-12 \\ \Leftrightarrow -2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{-2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(4x^2+0=0 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-3x^2+9=4x^2+2 \\ \Leftrightarrow -3x^2-4x^2=2-9 \\ \Leftrightarrow -7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{-7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(-5x^2+605=0 \\ \Leftrightarrow -5x^2 = -605 \\ \Leftrightarrow x^2 = \frac{-605}{-5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-7x^2+33=-8x^2-3 \\ \Leftrightarrow -7x^2+8x^2=-3-33 \\ \Leftrightarrow x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(4(-4x^2-7)=-(8x^2+1596) \\ \Leftrightarrow -16x^2-28=-8x^2-1596 \\ \Leftrightarrow -16x^2+8x^2=-1596+28 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(3x^2-588=0 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(-7x^2+112=0 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)