Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-6x^2-5)=-(-7x^2-190)\)
2. \(3x^2+10=2x^2+6\)
3. \(x^2-1=0\)
4. \(6x^2-726=0\)
5. \(-4x^2+400=0\)
6. \(5(10x^2+6)=-(-49x^2-14)\)
7. \(3(8x^2+7)=-(-26x^2-13)\)
8. \(-11x^2+1578=-4x^2+3\)
9. \(-4x^2+1158=4x^2+6\)
10. \(4(5x^2+7)=-(-27x^2-1036)\)
11. \(3x^2+12=0\)
12. \(3x^2+134=8x^2+9\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-6x^2-5)=-(-7x^2-190) \\ \Leftrightarrow 12x^2+10=7x^2+190 \\ \Leftrightarrow 12x^2-7x^2=190-10 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(3x^2+10=2x^2+6 \\ \Leftrightarrow 3x^2-2x^2=6-10 \\ \Leftrightarrow x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(x^2-1=0 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(6x^2-726=0 \\ \Leftrightarrow 6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(-4x^2+400=0 \\ \Leftrightarrow -4x^2 = -400 \\ \Leftrightarrow x^2 = \frac{-400}{-4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(5(10x^2+6)=-(-49x^2-14) \\ \Leftrightarrow 50x^2+30=49x^2+14 \\ \Leftrightarrow 50x^2-49x^2=14-30 \\ \Leftrightarrow x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(3(8x^2+7)=-(-26x^2-13) \\ \Leftrightarrow 24x^2+21=26x^2+13 \\ \Leftrightarrow 24x^2-26x^2=13-21 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(-11x^2+1578=-4x^2+3 \\ \Leftrightarrow -11x^2+4x^2=3-1578 \\ \Leftrightarrow -7x^2 = -1575 \\ \Leftrightarrow x^2 = \frac{-1575}{-7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
9. \(-4x^2+1158=4x^2+6 \\ \Leftrightarrow -4x^2-4x^2=6-1158 \\ \Leftrightarrow -8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
10. \(4(5x^2+7)=-(-27x^2-1036) \\ \Leftrightarrow 20x^2+28=27x^2+1036 \\ \Leftrightarrow 20x^2-27x^2=1036-28 \\ \Leftrightarrow -7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{-7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(3x^2+12=0 \\ \Leftrightarrow 3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3x^2+134=8x^2+9 \\ \Leftrightarrow 3x^2-8x^2=9-134 \\ \Leftrightarrow -5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{-5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)