Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-49=0\)
2. \(-5(-7x^2-5)=-(-37x^2-475)\)
3. \(-7x^2+898=-3x^2-2\)
4. \(-x^2+81=0\)
5. \(-3x^2+0=0\)
6. \(-17x^2+134=-9x^2+6\)
7. \(2x^2+0=0\)
8. \(12x^2+329=10x^2-9\)
9. \(6x^2-864=0\)
10. \(7x^2-250=5x^2-8\)
11. \(-4(8x^2-8)=-(33x^2-48)\)
12. \(3(-5x^2-10)=-(16x^2+111)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-49=0 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(-5(-7x^2-5)=-(-37x^2-475) \\ \Leftrightarrow 35x^2+25=37x^2+475 \\ \Leftrightarrow 35x^2-37x^2=475-25 \\ \Leftrightarrow -2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{-2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-7x^2+898=-3x^2-2 \\ \Leftrightarrow -7x^2+3x^2=-2-898 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(-x^2+81=0 \\ \Leftrightarrow -x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{-1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(-3x^2+0=0 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-17x^2+134=-9x^2+6 \\ \Leftrightarrow -17x^2+9x^2=6-134 \\ \Leftrightarrow -8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(2x^2+0=0 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(12x^2+329=10x^2-9 \\ \Leftrightarrow 12x^2-10x^2=-9-329 \\ \Leftrightarrow 2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(6x^2-864=0 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
10. \(7x^2-250=5x^2-8 \\ \Leftrightarrow 7x^2-5x^2=-8+250 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-4(8x^2-8)=-(33x^2-48) \\ \Leftrightarrow -32x^2+32=-33x^2+48 \\ \Leftrightarrow -32x^2+33x^2=48-32 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(3(-5x^2-10)=-(16x^2+111) \\ \Leftrightarrow -15x^2-30=-16x^2-111 \\ \Leftrightarrow -15x^2+16x^2=-111+30 \\ \Leftrightarrow x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{1} < 0 \\ V = \varnothing \\ -----------------\)