Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-3=4x^2-3\)
2. \(7x^2-1008=0\)
3. \(3x^2-75=0\)
4. \(-4(4x^2-4)=-(10x^2+80)\)
5. \(2x^2+288=0\)
6. \(-5x^2-80=0\)
7. \(-8x^2-86=-9x^2-5\)
8. \(-5x^2-180=0\)
9. \(-9x^2-31=-8x^2-6\)
10. \(5(9x^2+10)=-(-46x^2+94)\)
11. \(-8x^2+800=0\)
12. \(2x^2+242=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-3=4x^2-3 \\ \Leftrightarrow x^2-4x^2=-3+3 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(7x^2-1008=0 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(3x^2-75=0 \\ \Leftrightarrow 3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(-4(4x^2-4)=-(10x^2+80) \\ \Leftrightarrow -16x^2+16=-10x^2-80 \\ \Leftrightarrow -16x^2+10x^2=-80-16 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
5. \(2x^2+288=0 \\ \Leftrightarrow 2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5x^2-80=0 \\ \Leftrightarrow -5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{-5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-8x^2-86=-9x^2-5 \\ \Leftrightarrow -8x^2+9x^2=-5+86 \\ \Leftrightarrow x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(-5x^2-180=0 \\ \Leftrightarrow -5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{-5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-9x^2-31=-8x^2-6 \\ \Leftrightarrow -9x^2+8x^2=-6+31 \\ \Leftrightarrow -x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{-1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(5(9x^2+10)=-(-46x^2+94) \\ \Leftrightarrow 45x^2+50=46x^2-94 \\ \Leftrightarrow 45x^2-46x^2=-94-50 \\ \Leftrightarrow -x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{-1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(-8x^2+800=0 \\ \Leftrightarrow -8x^2 = -800 \\ \Leftrightarrow x^2 = \frac{-800}{-8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(2x^2+242=0 \\ \Leftrightarrow 2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{2} < 0 \\ V = \varnothing \\ -----------------\)