Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-3x^2+8)=-(8x^2-24)\)
2. \(3x^2-507=0\)
3. \(-4(9x^2-7)=-(43x^2-476)\)
4. \(-6x^2+726=0\)
5. \(2(-2x^2+9)=-(10x^2-402)\)
6. \(5(4x^2+8)=-(-26x^2-46)\)
7. \(-7x^2-347=-5x^2-9\)
8. \(4x^2-100=0\)
9. \(-4x^2-570=-8x^2+6\)
10. \(11x^2-38=6x^2+7\)
11. \(2(-6x^2+4)=-(16x^2+776)\)
12. \(2x^2+450=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-3x^2+8)=-(8x^2-24) \\ \Leftrightarrow -9x^2+24=-8x^2+24 \\ \Leftrightarrow -9x^2+8x^2=24-24 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(3x^2-507=0 \\ \Leftrightarrow 3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(-4(9x^2-7)=-(43x^2-476) \\ \Leftrightarrow -36x^2+28=-43x^2+476 \\ \Leftrightarrow -36x^2+43x^2=476-28 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-6x^2+726=0 \\ \Leftrightarrow -6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{-6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(2(-2x^2+9)=-(10x^2-402) \\ \Leftrightarrow -4x^2+18=-10x^2+402 \\ \Leftrightarrow -4x^2+10x^2=402-18 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
6. \(5(4x^2+8)=-(-26x^2-46) \\ \Leftrightarrow 20x^2+40=26x^2+46 \\ \Leftrightarrow 20x^2-26x^2=46-40 \\ \Leftrightarrow -6x^2 = 6 \\ \Leftrightarrow x^2 = \frac{6}{-6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-7x^2-347=-5x^2-9 \\ \Leftrightarrow -7x^2+5x^2=-9+347 \\ \Leftrightarrow -2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(4x^2-100=0 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
9. \(-4x^2-570=-8x^2+6 \\ \Leftrightarrow -4x^2+8x^2=6+570 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
10. \(11x^2-38=6x^2+7 \\ \Leftrightarrow 11x^2-6x^2=7+38 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(2(-6x^2+4)=-(16x^2+776) \\ \Leftrightarrow -12x^2+8=-16x^2-776 \\ \Leftrightarrow -12x^2+16x^2=-776-8 \\ \Leftrightarrow 4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2x^2+450=0 \\ \Leftrightarrow 2x^2 = -450 \\ \Leftrightarrow x^2 = \frac{-450}{2} < 0 \\ V = \varnothing \\ -----------------\)