Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2+36=6x^2+8\)
2. \(-9x^2+220=-3x^2+4\)
3. \(3x^2-243=0\)
4. \(7x^2-8=5x^2+10\)
5. \(-4x^2-36=0\)
6. \(8x^2-968=0\)
7. \(2x^2+5=-5x^2-2\)
8. \(-3(-3x^2-9)=-(-16x^2-1035)\)
9. \(x^2+1009=7x^2-5\)
10. \(-4(-3x^2-5)=-(-17x^2-340)\)
11. \(-13x^2+443=-6x^2-5\)
12. \(9x^2-6=7x^2-6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2+36=6x^2+8 \\ \Leftrightarrow -x^2-6x^2=8-36 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(-9x^2+220=-3x^2+4 \\ \Leftrightarrow -9x^2+3x^2=4-220 \\ \Leftrightarrow -6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{-6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(3x^2-243=0 \\ \Leftrightarrow 3x^2 = 243 \\ \Leftrightarrow x^2 = \frac{243}{3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(7x^2-8=5x^2+10 \\ \Leftrightarrow 7x^2-5x^2=10+8 \\ \Leftrightarrow 2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
5. \(-4x^2-36=0 \\ \Leftrightarrow -4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(8x^2-968=0 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(2x^2+5=-5x^2-2 \\ \Leftrightarrow 2x^2+5x^2=-2-5 \\ \Leftrightarrow 7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3(-3x^2-9)=-(-16x^2-1035) \\ \Leftrightarrow 9x^2+27=16x^2+1035 \\ \Leftrightarrow 9x^2-16x^2=1035-27 \\ \Leftrightarrow -7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{-7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(x^2+1009=7x^2-5 \\ \Leftrightarrow x^2-7x^2=-5-1009 \\ \Leftrightarrow -6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{-6}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(-4(-3x^2-5)=-(-17x^2-340) \\ \Leftrightarrow 12x^2+20=17x^2+340 \\ \Leftrightarrow 12x^2-17x^2=340-20 \\ \Leftrightarrow -5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{-5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-13x^2+443=-6x^2-5 \\ \Leftrightarrow -13x^2+6x^2=-5-443 \\ \Leftrightarrow -7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{-7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(9x^2-6=7x^2-6 \\ \Leftrightarrow 9x^2-7x^2=-6+6 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)