Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2-100=0\)
2. \(4(5x^2-7)=-(-12x^2+36)\)
3. \(3x^2+108=0\)
4. \(6x^2-5=2x^2-5\)
5. \(-9x^2+290=-6x^2-10\)
6. \(-x^2+49=0\)
7. \(-4x^2-676=0\)
8. \(4(8x^2-3)=-(-34x^2+174)\)
9. \(-x^2+0=0\)
10. \(-8x^2+968=0\)
11. \(-9x^2-5=-10x^2+4\)
12. \(-5(-4x^2-10)=-(-25x^2+795)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2-100=0 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
2. \(4(5x^2-7)=-(-12x^2+36) \\ \Leftrightarrow 20x^2-28=12x^2-36 \\ \Leftrightarrow 20x^2-12x^2=-36+28 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(3x^2+108=0 \\ \Leftrightarrow 3x^2 = -108 \\ \Leftrightarrow x^2 = \frac{-108}{3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(6x^2-5=2x^2-5 \\ \Leftrightarrow 6x^2-2x^2=-5+5 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-9x^2+290=-6x^2-10 \\ \Leftrightarrow -9x^2+6x^2=-10-290 \\ \Leftrightarrow -3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{-3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(-x^2+49=0 \\ \Leftrightarrow -x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{-1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-4x^2-676=0 \\ \Leftrightarrow -4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{-4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(4(8x^2-3)=-(-34x^2+174) \\ \Leftrightarrow 32x^2-12=34x^2-174 \\ \Leftrightarrow 32x^2-34x^2=-174+12 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(-x^2+0=0 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-8x^2+968=0 \\ \Leftrightarrow -8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{-8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-9x^2-5=-10x^2+4 \\ \Leftrightarrow -9x^2+10x^2=4+5 \\ \Leftrightarrow x^2 = 9 \\ \Leftrightarrow x^2 = \frac{9}{1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(-5(-4x^2-10)=-(-25x^2+795) \\ \Leftrightarrow 20x^2+50=25x^2-795 \\ \Leftrightarrow 20x^2-25x^2=-795-50 \\ \Leftrightarrow -5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{-5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)