Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2-1800=0\)
2. \(8x^2-8=0\)
3. \(5x^2+83=6x^2+2\)
4. \(3(4x^2+10)=-(-9x^2-30)\)
5. \(2x^2-242=0\)
6. \(3(-7x^2+8)=-(17x^2+40)\)
7. \(6x^2+1014=0\)
8. \(5x^2+69=6x^2+5\)
9. \(2x^2+109=9x^2-3\)
10. \(-14x^2+88=-8x^2-8\)
11. \(-5x^2-183=-10x^2-3\)
12. \(-x^2+9=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2-1800=0 \\ \Leftrightarrow 8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(8x^2-8=0 \\ \Leftrightarrow 8x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(5x^2+83=6x^2+2 \\ \Leftrightarrow 5x^2-6x^2=2-83 \\ \Leftrightarrow -x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{-1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(3(4x^2+10)=-(-9x^2-30) \\ \Leftrightarrow 12x^2+30=9x^2+30 \\ \Leftrightarrow 12x^2-9x^2=30-30 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(2x^2-242=0 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
6. \(3(-7x^2+8)=-(17x^2+40) \\ \Leftrightarrow -21x^2+24=-17x^2-40 \\ \Leftrightarrow -21x^2+17x^2=-40-24 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(6x^2+1014=0 \\ \Leftrightarrow 6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{6} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5x^2+69=6x^2+5 \\ \Leftrightarrow 5x^2-6x^2=5-69 \\ \Leftrightarrow -x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(2x^2+109=9x^2-3 \\ \Leftrightarrow 2x^2-9x^2=-3-109 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
10. \(-14x^2+88=-8x^2-8 \\ \Leftrightarrow -14x^2+8x^2=-8-88 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-5x^2-183=-10x^2-3 \\ \Leftrightarrow -5x^2+10x^2=-3+183 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(-x^2+9=0 \\ \Leftrightarrow -x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{-1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)