Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2-726=0\)
2. \(-8x^2-648=0\)
3. \(2x^2+242=0\)
4. \(5(6x^2-6)=-(-35x^2+30)\)
5. \(4x^2+870=-2x^2+6\)
6. \(9x^2-8=5x^2-8\)
7. \(-8x^2+288=0\)
8. \(2x^2-32=0\)
9. \(3x^2-48=0\)
10. \(x^2-254=5x^2+2\)
11. \(-5x^2-125=0\)
12. \(2(10x^2-10)=-(-15x^2-700)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2-726=0 \\ \Leftrightarrow -6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{-6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-8x^2-648=0 \\ \Leftrightarrow -8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{-8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2x^2+242=0 \\ \Leftrightarrow 2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5(6x^2-6)=-(-35x^2+30) \\ \Leftrightarrow 30x^2-30=35x^2-30 \\ \Leftrightarrow 30x^2-35x^2=-30+30 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(4x^2+870=-2x^2+6 \\ \Leftrightarrow 4x^2+2x^2=6-870 \\ \Leftrightarrow 6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(9x^2-8=5x^2-8 \\ \Leftrightarrow 9x^2-5x^2=-8+8 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-8x^2+288=0 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(2x^2-32=0 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(3x^2-48=0 \\ \Leftrightarrow 3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
10. \(x^2-254=5x^2+2 \\ \Leftrightarrow x^2-5x^2=2+254 \\ \Leftrightarrow -4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{-4} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-5x^2-125=0 \\ \Leftrightarrow -5x^2 = 125 \\ \Leftrightarrow x^2 = \frac{125}{-5} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2(10x^2-10)=-(-15x^2-700) \\ \Leftrightarrow 20x^2-20=15x^2+700 \\ \Leftrightarrow 20x^2-15x^2=700+20 \\ \Leftrightarrow 5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)