Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-676=0\)
2. \(-2(-6x^2+6)=-(-10x^2+12)\)
3. \(-2x^2+1189=5x^2+6\)
4. \(3x^2-698=-4x^2+2\)
5. \(-2x^2+18=0\)
6. \(-4(9x^2-10)=-(28x^2-40)\)
7. \(-3(-9x^2+4)=-(-20x^2+712)\)
8. \(-7x^2-1183=0\)
9. \(5(-2x^2-6)=-(15x^2+35)\)
10. \(5x^2-1125=0\)
11. \(2x^2-162=0\)
12. \(-4x^2+900=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-676=0 \\ \Leftrightarrow -4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{-4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-2(-6x^2+6)=-(-10x^2+12) \\ \Leftrightarrow 12x^2-12=10x^2-12 \\ \Leftrightarrow 12x^2-10x^2=-12+12 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-2x^2+1189=5x^2+6 \\ \Leftrightarrow -2x^2-5x^2=6-1189 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(3x^2-698=-4x^2+2 \\ \Leftrightarrow 3x^2+4x^2=2+698 \\ \Leftrightarrow 7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(-2x^2+18=0 \\ \Leftrightarrow -2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{-2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(-4(9x^2-10)=-(28x^2-40) \\ \Leftrightarrow -36x^2+40=-28x^2+40 \\ \Leftrightarrow -36x^2+28x^2=40-40 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-3(-9x^2+4)=-(-20x^2+712) \\ \Leftrightarrow 27x^2-12=20x^2-712 \\ \Leftrightarrow 27x^2-20x^2=-712+12 \\ \Leftrightarrow 7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-7x^2-1183=0 \\ \Leftrightarrow -7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{-7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(5(-2x^2-6)=-(15x^2+35) \\ \Leftrightarrow -10x^2-30=-15x^2-35 \\ \Leftrightarrow -10x^2+15x^2=-35+30 \\ \Leftrightarrow 5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(5x^2-1125=0 \\ \Leftrightarrow 5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(2x^2-162=0 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
12. \(-4x^2+900=0 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)