Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(10x^2+3)=-(34x^2-891)\)
2. \(-2(4x^2-10)=-(11x^2+88)\)
3. \(x^2+43=-4x^2-2\)
4. \(2(-7x^2+5)=-(18x^2+474)\)
5. \(2(-6x^2+6)=-(5x^2+1563)\)
6. \(-2x^2+0=0\)
7. \(-3(6x^2+4)=-(26x^2+980)\)
8. \(-5(2x^2+4)=-(18x^2+20)\)
9. \(5(-10x^2-4)=-(56x^2+44)\)
10. \(5x^2-195=8x^2-3\)
11. \(2(4x^2-5)=-(-14x^2+610)\)
12. \(-10x^2-91=-8x^2+7\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(10x^2+3)=-(34x^2-891) \\ \Leftrightarrow -30x^2-9=-34x^2+891 \\ \Leftrightarrow -30x^2+34x^2=891+9 \\ \Leftrightarrow 4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(-2(4x^2-10)=-(11x^2+88) \\ \Leftrightarrow -8x^2+20=-11x^2-88 \\ \Leftrightarrow -8x^2+11x^2=-88-20 \\ \Leftrightarrow 3x^2 = -108 \\ \Leftrightarrow x^2 = \frac{-108}{3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(x^2+43=-4x^2-2 \\ \Leftrightarrow x^2+4x^2=-2-43 \\ \Leftrightarrow 5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2(-7x^2+5)=-(18x^2+474) \\ \Leftrightarrow -14x^2+10=-18x^2-474 \\ \Leftrightarrow -14x^2+18x^2=-474-10 \\ \Leftrightarrow 4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2(-6x^2+6)=-(5x^2+1563) \\ \Leftrightarrow -12x^2+12=-5x^2-1563 \\ \Leftrightarrow -12x^2+5x^2=-1563-12 \\ \Leftrightarrow -7x^2 = -1575 \\ \Leftrightarrow x^2 = \frac{-1575}{-7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(-2x^2+0=0 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-3(6x^2+4)=-(26x^2+980) \\ \Leftrightarrow -18x^2-12=-26x^2-980 \\ \Leftrightarrow -18x^2+26x^2=-980+12 \\ \Leftrightarrow 8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-5(2x^2+4)=-(18x^2+20) \\ \Leftrightarrow -10x^2-20=-18x^2-20 \\ \Leftrightarrow -10x^2+18x^2=-20+20 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(5(-10x^2-4)=-(56x^2+44) \\ \Leftrightarrow -50x^2-20=-56x^2-44 \\ \Leftrightarrow -50x^2+56x^2=-44+20 \\ \Leftrightarrow 6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{6} < 0 \\ V = \varnothing \\ -----------------\)
10. \(5x^2-195=8x^2-3 \\ \Leftrightarrow 5x^2-8x^2=-3+195 \\ \Leftrightarrow -3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{-3} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2(4x^2-5)=-(-14x^2+610) \\ \Leftrightarrow 8x^2-10=14x^2-610 \\ \Leftrightarrow 8x^2-14x^2=-610+10 \\ \Leftrightarrow -6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{-6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(-10x^2-91=-8x^2+7 \\ \Leftrightarrow -10x^2+8x^2=7+91 \\ \Leftrightarrow -2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{-2} < 0 \\ V = \varnothing \\ -----------------\)