Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-4x^2-6)=-(18x^2+1194)\)
2. \(-x^2+0=0\)
3. \(4(-6x^2-2)=-(21x^2-235)\)
4. \(3x^2+12=0\)
5. \(-8x^2+118=-7x^2-3\)
6. \(x^2-100=0\)
7. \(4(4x^2+6)=-(-9x^2+424)\)
8. \(-5(-4x^2-9)=-(-26x^2-45)\)
9. \(11x^2+15=9x^2-3\)
10. \(-4x^2-900=0\)
11. \(-9x^2+458=-2x^2+10\)
12. \(5(-4x^2+4)=-(22x^2-308)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-4x^2-6)=-(18x^2+1194) \\ \Leftrightarrow -12x^2-18=-18x^2-1194 \\ \Leftrightarrow -12x^2+18x^2=-1194+18 \\ \Leftrightarrow 6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-x^2+0=0 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(4(-6x^2-2)=-(21x^2-235) \\ \Leftrightarrow -24x^2-8=-21x^2+235 \\ \Leftrightarrow -24x^2+21x^2=235+8 \\ \Leftrightarrow -3x^2 = 243 \\ \Leftrightarrow x^2 = \frac{243}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(3x^2+12=0 \\ \Leftrightarrow 3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-8x^2+118=-7x^2-3 \\ \Leftrightarrow -8x^2+7x^2=-3-118 \\ \Leftrightarrow -x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{-1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
6. \(x^2-100=0 \\ \Leftrightarrow x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(4(4x^2+6)=-(-9x^2+424) \\ \Leftrightarrow 16x^2+24=9x^2-424 \\ \Leftrightarrow 16x^2-9x^2=-424-24 \\ \Leftrightarrow 7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5(-4x^2-9)=-(-26x^2-45) \\ \Leftrightarrow 20x^2+45=26x^2+45 \\ \Leftrightarrow 20x^2-26x^2=45-45 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(11x^2+15=9x^2-3 \\ \Leftrightarrow 11x^2-9x^2=-3-15 \\ \Leftrightarrow 2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{2} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4x^2-900=0 \\ \Leftrightarrow -4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{-4} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-9x^2+458=-2x^2+10 \\ \Leftrightarrow -9x^2+2x^2=10-458 \\ \Leftrightarrow -7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{-7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(5(-4x^2+4)=-(22x^2-308) \\ \Leftrightarrow -20x^2+20=-22x^2+308 \\ \Leftrightarrow -20x^2+22x^2=308-20 \\ \Leftrightarrow 2x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)