Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-3x^2+2)=-(8x^2+248)\)
2. \(-4(-4x^2-10)=-(-19x^2+467)\)
3. \(4(-4x^2-6)=-(9x^2+1032)\)
4. \(-4(-6x^2-8)=-(-29x^2+948)\)
5. \(2(-10x^2-4)=-(28x^2+8)\)
6. \(-5x^2-91=-3x^2+7\)
7. \(7x^2-448=0\)
8. \(-8x^2+237=-6x^2-5\)
9. \(-4(4x^2-4)=-(22x^2-1192)\)
10. \(4x^2-1012=10x^2+2\)
11. \(-2(-9x^2-7)=-(-23x^2+486)\)
12. \(-11x^2-10=-9x^2-10\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-3x^2+2)=-(8x^2+248) \\ \Leftrightarrow -12x^2+8=-8x^2-248 \\ \Leftrightarrow -12x^2+8x^2=-248-8 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
2. \(-4(-4x^2-10)=-(-19x^2+467) \\ \Leftrightarrow 16x^2+40=19x^2-467 \\ \Leftrightarrow 16x^2-19x^2=-467-40 \\ \Leftrightarrow -3x^2 = -507 \\ \Leftrightarrow x^2 = \frac{-507}{-3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(4(-4x^2-6)=-(9x^2+1032) \\ \Leftrightarrow -16x^2-24=-9x^2-1032 \\ \Leftrightarrow -16x^2+9x^2=-1032+24 \\ \Leftrightarrow -7x^2 = -1008 \\ \Leftrightarrow x^2 = \frac{-1008}{-7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
4. \(-4(-6x^2-8)=-(-29x^2+948) \\ \Leftrightarrow 24x^2+32=29x^2-948 \\ \Leftrightarrow 24x^2-29x^2=-948-32 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(2(-10x^2-4)=-(28x^2+8) \\ \Leftrightarrow -20x^2-8=-28x^2-8 \\ \Leftrightarrow -20x^2+28x^2=-8+8 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-5x^2-91=-3x^2+7 \\ \Leftrightarrow -5x^2+3x^2=7+91 \\ \Leftrightarrow -2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{-2} < 0 \\ V = \varnothing \\ -----------------\)
7. \(7x^2-448=0 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-8x^2+237=-6x^2-5 \\ \Leftrightarrow -8x^2+6x^2=-5-237 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-4(4x^2-4)=-(22x^2-1192) \\ \Leftrightarrow -16x^2+16=-22x^2+1192 \\ \Leftrightarrow -16x^2+22x^2=1192-16 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(4x^2-1012=10x^2+2 \\ \Leftrightarrow 4x^2-10x^2=2+1012 \\ \Leftrightarrow -6x^2 = 1014 \\ \Leftrightarrow x^2 = \frac{1014}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-2(-9x^2-7)=-(-23x^2+486) \\ \Leftrightarrow 18x^2+14=23x^2-486 \\ \Leftrightarrow 18x^2-23x^2=-486-14 \\ \Leftrightarrow -5x^2 = -500 \\ \Leftrightarrow x^2 = \frac{-500}{-5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(-11x^2-10=-9x^2-10 \\ \Leftrightarrow -11x^2+9x^2=-10+10 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)