Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2-12=0\)
2. \(7x^2-1372=0\)
3. \(3x^2+507=0\)
4. \(-3x^2-108=0\)
5. \(-3(-3x^2+2)=-(-2x^2-694)\)
6. \(-x^2-6=3x^2+10\)
7. \(2(4x^2-5)=-(-13x^2+30)\)
8. \(3x^2-192=0\)
9. \(-9x^2-8=-10x^2-7\)
10. \(-x^2-1=0\)
11. \(-4x^2-843=-9x^2+2\)
12. \(-7x^2+28=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2-12=0 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(7x^2-1372=0 \\ \Leftrightarrow 7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(3x^2+507=0 \\ \Leftrightarrow 3x^2 = -507 \\ \Leftrightarrow x^2 = \frac{-507}{3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-3x^2-108=0 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(-3x^2+2)=-(-2x^2-694) \\ \Leftrightarrow 9x^2-6=2x^2+694 \\ \Leftrightarrow 9x^2-2x^2=694+6 \\ \Leftrightarrow 7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(-x^2-6=3x^2+10 \\ \Leftrightarrow -x^2-3x^2=10+6 \\ \Leftrightarrow -4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-4} < 0 \\ V = \varnothing \\ -----------------\)
7. \(2(4x^2-5)=-(-13x^2+30) \\ \Leftrightarrow 8x^2-10=13x^2-30 \\ \Leftrightarrow 8x^2-13x^2=-30+10 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(3x^2-192=0 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(-9x^2-8=-10x^2-7 \\ \Leftrightarrow -9x^2+10x^2=-7+8 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
10. \(-x^2-1=0 \\ \Leftrightarrow -x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{-1} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4x^2-843=-9x^2+2 \\ \Leftrightarrow -4x^2+9x^2=2+843 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-7x^2+28=0 \\ \Leftrightarrow -7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{-7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)