Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+96=0\)
2. \(2(-3x^2-4)=-(0x^2+1358)\)
3. \(4(9x^2+3)=-(-43x^2+100)\)
4. \(-3(-8x^2+4)=-(-22x^2+12)\)
5. \(-4(4x^2+5)=-(18x^2-78)\)
6. \(x^2-16=0\)
7. \(-4(4x^2+5)=-(14x^2-222)\)
8. \(5x^2-80=0\)
9. \(-12x^2+22=-9x^2+10\)
10. \(-6x^2-600=0\)
11. \(2x^2-2=-2x^2-2\)
12. \(-3x^2+48=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+96=0 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(2(-3x^2-4)=-(0x^2+1358) \\ \Leftrightarrow -6x^2-8=0x^2-1358 \\ \Leftrightarrow -6x^2+0x^2=-1358+8 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
3. \(4(9x^2+3)=-(-43x^2+100) \\ \Leftrightarrow 36x^2+12=43x^2-100 \\ \Leftrightarrow 36x^2-43x^2=-100-12 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(-3(-8x^2+4)=-(-22x^2+12) \\ \Leftrightarrow 24x^2-12=22x^2-12 \\ \Leftrightarrow 24x^2-22x^2=-12+12 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-4(4x^2+5)=-(18x^2-78) \\ \Leftrightarrow -16x^2-20=-18x^2+78 \\ \Leftrightarrow -16x^2+18x^2=78+20 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(x^2-16=0 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-4(4x^2+5)=-(14x^2-222) \\ \Leftrightarrow -16x^2-20=-14x^2+222 \\ \Leftrightarrow -16x^2+14x^2=222+20 \\ \Leftrightarrow -2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5x^2-80=0 \\ \Leftrightarrow 5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(-12x^2+22=-9x^2+10 \\ \Leftrightarrow -12x^2+9x^2=10-22 \\ \Leftrightarrow -3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{-3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-6x^2-600=0 \\ \Leftrightarrow -6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{-6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2x^2-2=-2x^2-2 \\ \Leftrightarrow 2x^2+2x^2=-2+2 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-3x^2+48=0 \\ \Leftrightarrow -3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{-3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)