Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2+384=0\)
2. \(5x^2-180=0\)
3. \(-6x^2-66=-10x^2-2\)
4. \(-2(-2x^2-10)=-(3x^2+8)\)
5. \(-x^2+100=0\)
6. \(15x^2-394=7x^2-2\)
7. \(4(-3x^2-7)=-(14x^2-422)\)
8. \(-3(-6x^2-5)=-(-14x^2-799)\)
9. \(5(8x^2-7)=-(-41x^2+60)\)
10. \(14x^2-51=8x^2+3\)
11. \(-3(4x^2-2)=-(18x^2+858)\)
12. \(11x^2+720=5x^2-6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2+384=0 \\ \Leftrightarrow 6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(5x^2-180=0 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(-6x^2-66=-10x^2-2 \\ \Leftrightarrow -6x^2+10x^2=-2+66 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(-2(-2x^2-10)=-(3x^2+8) \\ \Leftrightarrow 4x^2+20=-3x^2-8 \\ \Leftrightarrow 4x^2+3x^2=-8-20 \\ \Leftrightarrow 7x^2 = -28 \\ \Leftrightarrow x^2 = \frac{-28}{7} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-x^2+100=0 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(15x^2-394=7x^2-2 \\ \Leftrightarrow 15x^2-7x^2=-2+394 \\ \Leftrightarrow 8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(4(-3x^2-7)=-(14x^2-422) \\ \Leftrightarrow -12x^2-28=-14x^2+422 \\ \Leftrightarrow -12x^2+14x^2=422+28 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(-3(-6x^2-5)=-(-14x^2-799) \\ \Leftrightarrow 18x^2+15=14x^2+799 \\ \Leftrightarrow 18x^2-14x^2=799-15 \\ \Leftrightarrow 4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(5(8x^2-7)=-(-41x^2+60) \\ \Leftrightarrow 40x^2-35=41x^2-60 \\ \Leftrightarrow 40x^2-41x^2=-60+35 \\ \Leftrightarrow -x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{-1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(14x^2-51=8x^2+3 \\ \Leftrightarrow 14x^2-8x^2=3+51 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(-3(4x^2-2)=-(18x^2+858) \\ \Leftrightarrow -12x^2+6=-18x^2-858 \\ \Leftrightarrow -12x^2+18x^2=-858-6 \\ \Leftrightarrow 6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(11x^2+720=5x^2-6 \\ \Leftrightarrow 11x^2-5x^2=-6-720 \\ \Leftrightarrow 6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{6} < 0 \\ V = \varnothing \\ -----------------\)