Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2+2=6x^2+2\)
2. \(8x^2+8=0\)
3. \(4(6x^2+7)=-(-21x^2+272)\)
4. \(-5(4x^2-7)=-(22x^2-67)\)
5. \(8x^2-128=0\)
6. \(3x^2-9=-4x^2-9\)
7. \(4(-9x^2-8)=-(38x^2+32)\)
8. \(-6x^2+13=-9x^2+10\)
9. \(-4(10x^2-2)=-(43x^2-155)\)
10. \(-2x^2+6=-6x^2+10\)
11. \(10x^2-126=9x^2-5\)
12. \(4x^2+8=7x^2+8\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2+2=6x^2+2 \\ \Leftrightarrow 7x^2-6x^2=2-2 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(8x^2+8=0 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(4(6x^2+7)=-(-21x^2+272) \\ \Leftrightarrow 24x^2+28=21x^2-272 \\ \Leftrightarrow 24x^2-21x^2=-272-28 \\ \Leftrightarrow 3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-5(4x^2-7)=-(22x^2-67) \\ \Leftrightarrow -20x^2+35=-22x^2+67 \\ \Leftrightarrow -20x^2+22x^2=67-35 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
5. \(8x^2-128=0 \\ \Leftrightarrow 8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(3x^2-9=-4x^2-9 \\ \Leftrightarrow 3x^2+4x^2=-9+9 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(4(-9x^2-8)=-(38x^2+32) \\ \Leftrightarrow -36x^2-32=-38x^2-32 \\ \Leftrightarrow -36x^2+38x^2=-32+32 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-6x^2+13=-9x^2+10 \\ \Leftrightarrow -6x^2+9x^2=10-13 \\ \Leftrightarrow 3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-4(10x^2-2)=-(43x^2-155) \\ \Leftrightarrow -40x^2+8=-43x^2+155 \\ \Leftrightarrow -40x^2+43x^2=155-8 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(-2x^2+6=-6x^2+10 \\ \Leftrightarrow -2x^2+6x^2=10-6 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
11. \(10x^2-126=9x^2-5 \\ \Leftrightarrow 10x^2-9x^2=-5+126 \\ \Leftrightarrow x^2 = 121 \\ \Leftrightarrow x^2 = \frac{121}{1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
12. \(4x^2+8=7x^2+8 \\ \Leftrightarrow 4x^2-7x^2=8-8 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)