Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-2x^2+2)=-(3x^2-1571)\)
2. \(-3(4x^2+7)=-(6x^2-195)\)
3. \(6x^2-216=0\)
4. \(4x^2-156=10x^2-6\)
5. \(-x^2+0=0\)
6. \(10x^2-246=8x^2-4\)
7. \(5(3x^2-10)=-(-8x^2+225)\)
8. \(x^2-148=-3x^2-4\)
9. \(x^2-2=3x^2-10\)
10. \(-6x^2+0=0\)
11. \(-3(-7x^2-5)=-(-24x^2-315)\)
12. \(-3x^2-69=-2x^2-5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-2x^2+2)=-(3x^2-1571) \\ \Leftrightarrow 4x^2-4=-3x^2+1571 \\ \Leftrightarrow 4x^2+3x^2=1571+4 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(-3(4x^2+7)=-(6x^2-195) \\ \Leftrightarrow -12x^2-21=-6x^2+195 \\ \Leftrightarrow -12x^2+6x^2=195+21 \\ \Leftrightarrow -6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{-6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(6x^2-216=0 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(4x^2-156=10x^2-6 \\ \Leftrightarrow 4x^2-10x^2=-6+156 \\ \Leftrightarrow -6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{-6} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-x^2+0=0 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(10x^2-246=8x^2-4 \\ \Leftrightarrow 10x^2-8x^2=-4+246 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(5(3x^2-10)=-(-8x^2+225) \\ \Leftrightarrow 15x^2-50=8x^2-225 \\ \Leftrightarrow 15x^2-8x^2=-225+50 \\ \Leftrightarrow 7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(x^2-148=-3x^2-4 \\ \Leftrightarrow x^2+3x^2=-4+148 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
9. \(x^2-2=3x^2-10 \\ \Leftrightarrow x^2-3x^2=-10+2 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-6x^2+0=0 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-3(-7x^2-5)=-(-24x^2-315) \\ \Leftrightarrow 21x^2+15=24x^2+315 \\ \Leftrightarrow 21x^2-24x^2=315-15 \\ \Leftrightarrow -3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{-3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-3x^2-69=-2x^2-5 \\ \Leftrightarrow -3x^2+2x^2=-5+69 \\ \Leftrightarrow -x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{-1} < 0 \\ V = \varnothing \\ -----------------\)