Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2-252=0\)
2. \(-4x^2-598=-10x^2+2\)
3. \(6x^2+1014=0\)
4. \(3(4x^2+8)=-(-19x^2-276)\)
5. \(4x^2+872=10x^2+8\)
6. \(12x^2+1377=5x^2+5\)
7. \(13x^2+779=9x^2-5\)
8. \(-6x^2+456=-8x^2+6\)
9. \(10x^2+1793=2x^2-7\)
10. \(-3(-6x^2-2)=-(-16x^2-6)\)
11. \(-2(-4x^2-4)=-(-5x^2-8)\)
12. \(6x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2-252=0 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(-4x^2-598=-10x^2+2 \\ \Leftrightarrow -4x^2+10x^2=2+598 \\ \Leftrightarrow 6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(6x^2+1014=0 \\ \Leftrightarrow 6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{6} < 0 \\ V = \varnothing \\ -----------------\)
4. \(3(4x^2+8)=-(-19x^2-276) \\ \Leftrightarrow 12x^2+24=19x^2+276 \\ \Leftrightarrow 12x^2-19x^2=276-24 \\ \Leftrightarrow -7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{-7} < 0 \\ V = \varnothing \\ -----------------\)
5. \(4x^2+872=10x^2+8 \\ \Leftrightarrow 4x^2-10x^2=8-872 \\ \Leftrightarrow -6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{-6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(12x^2+1377=5x^2+5 \\ \Leftrightarrow 12x^2-5x^2=5-1377 \\ \Leftrightarrow 7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{7} < 0 \\ V = \varnothing \\ -----------------\)
7. \(13x^2+779=9x^2-5 \\ \Leftrightarrow 13x^2-9x^2=-5-779 \\ \Leftrightarrow 4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-6x^2+456=-8x^2+6 \\ \Leftrightarrow -6x^2+8x^2=6-456 \\ \Leftrightarrow 2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(10x^2+1793=2x^2-7 \\ \Leftrightarrow 10x^2-2x^2=-7-1793 \\ \Leftrightarrow 8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-3(-6x^2-2)=-(-16x^2-6) \\ \Leftrightarrow 18x^2+6=16x^2+6 \\ \Leftrightarrow 18x^2-16x^2=6-6 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-2(-4x^2-4)=-(-5x^2-8) \\ \Leftrightarrow 8x^2+8=5x^2+8 \\ \Leftrightarrow 8x^2-5x^2=8-8 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)