Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(2x^2+5)=-(0x^2-586)\)
2. \(-2x^2+409=3x^2+4\)
3. \(-10x^2-3=-2x^2-3\)
4. \(3(6x^2+8)=-(-17x^2-24)\)
5. \(8x^2-1800=0\)
6. \(8x^2-1355=2x^2-5\)
7. \(-3(6x^2+9)=-(16x^2-45)\)
8. \(7x^2-112=0\)
9. \(-8x^2+1152=0\)
10. \(-2(-5x^2-10)=-(-3x^2-83)\)
11. \(-10x^2+120=-3x^2+8\)
12. \(6x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(2x^2+5)=-(0x^2-586) \\ \Leftrightarrow 4x^2+10=0x^2+586 \\ \Leftrightarrow 4x^2+0x^2=586-10 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
2. \(-2x^2+409=3x^2+4 \\ \Leftrightarrow -2x^2-3x^2=4-409 \\ \Leftrightarrow -5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{-5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
3. \(-10x^2-3=-2x^2-3 \\ \Leftrightarrow -10x^2+2x^2=-3+3 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(3(6x^2+8)=-(-17x^2-24) \\ \Leftrightarrow 18x^2+24=17x^2+24 \\ \Leftrightarrow 18x^2-17x^2=24-24 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(8x^2-1800=0 \\ \Leftrightarrow 8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(8x^2-1355=2x^2-5 \\ \Leftrightarrow 8x^2-2x^2=-5+1355 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(-3(6x^2+9)=-(16x^2-45) \\ \Leftrightarrow -18x^2-27=-16x^2+45 \\ \Leftrightarrow -18x^2+16x^2=45+27 \\ \Leftrightarrow -2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(7x^2-112=0 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(-8x^2+1152=0 \\ \Leftrightarrow -8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
10. \(-2(-5x^2-10)=-(-3x^2-83) \\ \Leftrightarrow 10x^2+20=3x^2+83 \\ \Leftrightarrow 10x^2-3x^2=83-20 \\ \Leftrightarrow 7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(-10x^2+120=-3x^2+8 \\ \Leftrightarrow -10x^2+3x^2=8-120 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)