Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+372=-7x^2+9\)
2. \(-4x^2-611=-9x^2-6\)
3. \(-6x^2+384=0\)
4. \(-2(-5x^2-3)=-(-13x^2+582)\)
5. \(-2(-5x^2+7)=-(-11x^2+63)\)
6. \(-8x^2-35=-10x^2-3\)
7. \(-6x^2+54=0\)
8. \(-13x^2+1576=-5x^2+8\)
9. \(4(10x^2+2)=-(-47x^2+839)\)
10. \(6x^2+24=0\)
11. \(5x^2-180=0\)
12. \(-3x^2+432=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+372=-7x^2+9 \\ \Leftrightarrow -4x^2+7x^2=9-372 \\ \Leftrightarrow 3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-4x^2-611=-9x^2-6 \\ \Leftrightarrow -4x^2+9x^2=-6+611 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(-6x^2+384=0 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(-2(-5x^2-3)=-(-13x^2+582) \\ \Leftrightarrow 10x^2+6=13x^2-582 \\ \Leftrightarrow 10x^2-13x^2=-582-6 \\ \Leftrightarrow -3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{-3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(-2(-5x^2+7)=-(-11x^2+63) \\ \Leftrightarrow 10x^2-14=11x^2-63 \\ \Leftrightarrow 10x^2-11x^2=-63+14 \\ \Leftrightarrow -x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{-1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(-8x^2-35=-10x^2-3 \\ \Leftrightarrow -8x^2+10x^2=-3+35 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-6x^2+54=0 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
8. \(-13x^2+1576=-5x^2+8 \\ \Leftrightarrow -13x^2+5x^2=8-1576 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(4(10x^2+2)=-(-47x^2+839) \\ \Leftrightarrow 40x^2+8=47x^2-839 \\ \Leftrightarrow 40x^2-47x^2=-839-8 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(6x^2+24=0 \\ \Leftrightarrow 6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{6} < 0 \\ V = \varnothing \\ -----------------\)
11. \(5x^2-180=0 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(-3x^2+432=0 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)