Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(-7x^2+7)=-(-38x^2+62)\)
2. \(14x^2-787=10x^2-3\)
3. \(-8x^2-8=-3x^2-8\)
4. \(-x^2+196=0\)
5. \(7x^2+28=0\)
6. \(-5(-6x^2+4)=-(-22x^2+20)\)
7. \(-14x^2+153=-8x^2+3\)
8. \(-8x^2-288=0\)
9. \(2x^2-98=0\)
10. \(6x^2-54=0\)
11. \(6x^2-294=0\)
12. \(-3x^2-48=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(-7x^2+7)=-(-38x^2+62) \\ \Leftrightarrow 35x^2-35=38x^2-62 \\ \Leftrightarrow 35x^2-38x^2=-62+35 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
2. \(14x^2-787=10x^2-3 \\ \Leftrightarrow 14x^2-10x^2=-3+787 \\ \Leftrightarrow 4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-8x^2-8=-3x^2-8 \\ \Leftrightarrow -8x^2+3x^2=-8+8 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-x^2+196=0 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(7x^2+28=0 \\ \Leftrightarrow 7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5(-6x^2+4)=-(-22x^2+20) \\ \Leftrightarrow 30x^2-20=22x^2-20 \\ \Leftrightarrow 30x^2-22x^2=-20+20 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-14x^2+153=-8x^2+3 \\ \Leftrightarrow -14x^2+8x^2=3-153 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(-8x^2-288=0 \\ \Leftrightarrow -8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(2x^2-98=0 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(6x^2-54=0 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(6x^2-294=0 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(-3x^2-48=0 \\ \Leftrightarrow -3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{-3} < 0 \\ V = \varnothing \\ -----------------\)