Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2+0=0\)
2. \(-4x^2+1132=-9x^2+7\)
3. \(-7x^2+7=0\)
4. \(4x^2+508=-4x^2-4\)
5. \(-x^2+16=0\)
6. \(-6x^2-96=0\)
7. \(-2x^2+72=0\)
8. \(-x^2-1342=-7x^2+8\)
9. \(-3(-6x^2-10)=-(-15x^2+558)\)
10. \(-4x^2+196=0\)
11. \(13x^2+3=9x^2+3\)
12. \(3(-4x^2+9)=-(17x^2-632)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2+0=0 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-4x^2+1132=-9x^2+7 \\ \Leftrightarrow -4x^2+9x^2=7-1132 \\ \Leftrightarrow 5x^2 = -1125 \\ \Leftrightarrow x^2 = \frac{-1125}{5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-7x^2+7=0 \\ \Leftrightarrow -7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{-7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(4x^2+508=-4x^2-4 \\ \Leftrightarrow 4x^2+4x^2=-4-508 \\ \Leftrightarrow 8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-x^2+16=0 \\ \Leftrightarrow -x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(-6x^2-96=0 \\ \Leftrightarrow -6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{-6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2x^2+72=0 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(-x^2-1342=-7x^2+8 \\ \Leftrightarrow -x^2+7x^2=8+1342 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
9. \(-3(-6x^2-10)=-(-15x^2+558) \\ \Leftrightarrow 18x^2+30=15x^2-558 \\ \Leftrightarrow 18x^2-15x^2=-558-30 \\ \Leftrightarrow 3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-4x^2+196=0 \\ \Leftrightarrow -4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(13x^2+3=9x^2+3 \\ \Leftrightarrow 13x^2-9x^2=3-3 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(3(-4x^2+9)=-(17x^2-632) \\ \Leftrightarrow -12x^2+27=-17x^2+632 \\ \Leftrightarrow -12x^2+17x^2=632-27 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)