Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(8x^2+3)=-(-19x^2+1116)\)
2. \(-2(-2x^2-5)=-(-12x^2-1810)\)
3. \(-x^2-43=-6x^2+2\)
4. \(3x^2+849=10x^2+2\)
5. \(4x^2-69=-4x^2+3\)
6. \(-4(6x^2-2)=-(16x^2-976)\)
7. \(x^2-49=0\)
8. \(11x^2-841=6x^2+4\)
9. \(-3x^2+243=0\)
10. \(6x^2-6=0\)
11. \(-11x^2+839=-6x^2-6\)
12. \(-7x^2-33=-6x^2+3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(8x^2+3)=-(-19x^2+1116) \\ \Leftrightarrow 24x^2+9=19x^2-1116 \\ \Leftrightarrow 24x^2-19x^2=-1116-9 \\ \Leftrightarrow 5x^2 = -1125 \\ \Leftrightarrow x^2 = \frac{-1125}{5} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-2(-2x^2-5)=-(-12x^2-1810) \\ \Leftrightarrow 4x^2+10=12x^2+1810 \\ \Leftrightarrow 4x^2-12x^2=1810-10 \\ \Leftrightarrow -8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{-8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-x^2-43=-6x^2+2 \\ \Leftrightarrow -x^2+6x^2=2+43 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(3x^2+849=10x^2+2 \\ \Leftrightarrow 3x^2-10x^2=2-849 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(4x^2-69=-4x^2+3 \\ \Leftrightarrow 4x^2+4x^2=3+69 \\ \Leftrightarrow 8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{8}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(-4(6x^2-2)=-(16x^2-976) \\ \Leftrightarrow -24x^2+8=-16x^2+976 \\ \Leftrightarrow -24x^2+16x^2=976-8 \\ \Leftrightarrow -8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{-8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(x^2-49=0 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(11x^2-841=6x^2+4 \\ \Leftrightarrow 11x^2-6x^2=4+841 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-3x^2+243=0 \\ \Leftrightarrow -3x^2 = -243 \\ \Leftrightarrow x^2 = \frac{-243}{-3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(6x^2-6=0 \\ \Leftrightarrow 6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
11. \(-11x^2+839=-6x^2-6 \\ \Leftrightarrow -11x^2+6x^2=-6-839 \\ \Leftrightarrow -5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{-5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(-7x^2-33=-6x^2+3 \\ \Leftrightarrow -7x^2+6x^2=3+33 \\ \Leftrightarrow -x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-1} < 0 \\ V = \varnothing \\ -----------------\)