Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2-336=6x^2+7\)
2. \(-2(2x^2+9)=-(8x^2-46)\)
3. \(2(3x^2-8)=-(-2x^2-384)\)
4. \(3x^2-300=0\)
5. \(-x^2+0=0\)
6. \(6x^2+131=7x^2+10\)
7. \(-12x^2-989=-7x^2-9\)
8. \(-5x^2+560=2x^2-7\)
9. \(-3(-6x^2-7)=-(-10x^2-13)\)
10. \(-2x^2+1178=5x^2-5\)
11. \(-8x^2+1800=0\)
12. \(3x^2+55=5x^2+5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2-336=6x^2+7 \\ \Leftrightarrow -x^2-6x^2=7+336 \\ \Leftrightarrow -7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{-7} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-2(2x^2+9)=-(8x^2-46) \\ \Leftrightarrow -4x^2-18=-8x^2+46 \\ \Leftrightarrow -4x^2+8x^2=46+18 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
3. \(2(3x^2-8)=-(-2x^2-384) \\ \Leftrightarrow 6x^2-16=2x^2+384 \\ \Leftrightarrow 6x^2-2x^2=384+16 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
4. \(3x^2-300=0 \\ \Leftrightarrow 3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(-x^2+0=0 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(6x^2+131=7x^2+10 \\ \Leftrightarrow 6x^2-7x^2=10-131 \\ \Leftrightarrow -x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{-1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(-12x^2-989=-7x^2-9 \\ \Leftrightarrow -12x^2+7x^2=-9+989 \\ \Leftrightarrow -5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{-5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5x^2+560=2x^2-7 \\ \Leftrightarrow -5x^2-2x^2=-7-560 \\ \Leftrightarrow -7x^2 = -567 \\ \Leftrightarrow x^2 = \frac{-567}{-7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(-3(-6x^2-7)=-(-10x^2-13) \\ \Leftrightarrow 18x^2+21=10x^2+13 \\ \Leftrightarrow 18x^2-10x^2=13-21 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2x^2+1178=5x^2-5 \\ \Leftrightarrow -2x^2-5x^2=-5-1178 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(-8x^2+1800=0 \\ \Leftrightarrow -8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
12. \(3x^2+55=5x^2+5 \\ \Leftrightarrow 3x^2-5x^2=5-55 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)