Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-4x^2-3)=-(4x^2+657)\)
2. \(6x^2+216=0\)
3. \(-11x^2+251=-8x^2+8\)
4. \(-8x^2+8=0\)
5. \(9x^2+13=5x^2-3\)
6. \(-4x^2+0=0\)
7. \(-2(4x^2-5)=-(x^2+1362)\)
8. \(2(-7x^2-6)=-(11x^2+375)\)
9. \(-4(-10x^2+5)=-(-46x^2+44)\)
10. \(4(-10x^2-2)=-(38x^2+136)\)
11. \(-3x^2+27=0\)
12. \(9x^2-91=5x^2+9\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-4x^2-3)=-(4x^2+657) \\ \Leftrightarrow -12x^2-9=-4x^2-657 \\ \Leftrightarrow -12x^2+4x^2=-657+9 \\ \Leftrightarrow -8x^2 = -648 \\ \Leftrightarrow x^2 = \frac{-648}{-8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(6x^2+216=0 \\ \Leftrightarrow 6x^2 = -216 \\ \Leftrightarrow x^2 = \frac{-216}{6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-11x^2+251=-8x^2+8 \\ \Leftrightarrow -11x^2+8x^2=8-251 \\ \Leftrightarrow -3x^2 = -243 \\ \Leftrightarrow x^2 = \frac{-243}{-3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(-8x^2+8=0 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(9x^2+13=5x^2-3 \\ \Leftrightarrow 9x^2-5x^2=-3-13 \\ \Leftrightarrow 4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-2(4x^2-5)=-(x^2+1362) \\ \Leftrightarrow -8x^2+10=-x^2-1362 \\ \Leftrightarrow -8x^2+x^2=-1362-10 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(2(-7x^2-6)=-(11x^2+375) \\ \Leftrightarrow -14x^2-12=-11x^2-375 \\ \Leftrightarrow -14x^2+11x^2=-375+12 \\ \Leftrightarrow -3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{-3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-4(-10x^2+5)=-(-46x^2+44) \\ \Leftrightarrow 40x^2-20=46x^2-44 \\ \Leftrightarrow 40x^2-46x^2=-44+20 \\ \Leftrightarrow -6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{-6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(4(-10x^2-2)=-(38x^2+136) \\ \Leftrightarrow -40x^2-8=-38x^2-136 \\ \Leftrightarrow -40x^2+38x^2=-136+8 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(-3x^2+27=0 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(9x^2-91=5x^2+9 \\ \Leftrightarrow 9x^2-5x^2=9+91 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)