Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(4x^2+6)=-(-18x^2+6)\)
2. \(x^2+9=8x^2+9\)
3. \(-4(4x^2+9)=-(19x^2-552)\)
4. \(-2x^2+128=0\)
5. \(13x^2-391=9x^2+9\)
6. \(7x^2-684=10x^2-9\)
7. \(5(6x^2-3)=-(-23x^2-832)\)
8. \(7x^2-1008=0\)
9. \(-2x^2-58=-5x^2-10\)
10. \(-2x^2+338=0\)
11. \(-3x^2-243=0\)
12. \(2(6x^2+2)=-(-7x^2-724)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(4x^2+6)=-(-18x^2+6) \\ \Leftrightarrow 12x^2+18=18x^2-6 \\ \Leftrightarrow 12x^2-18x^2=-6-18 \\ \Leftrightarrow -6x^2 = -24 \\ \Leftrightarrow x^2 = \frac{-24}{-6}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(x^2+9=8x^2+9 \\ \Leftrightarrow x^2-8x^2=9-9 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-4(4x^2+9)=-(19x^2-552) \\ \Leftrightarrow -16x^2-36=-19x^2+552 \\ \Leftrightarrow -16x^2+19x^2=552+36 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(-2x^2+128=0 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(13x^2-391=9x^2+9 \\ \Leftrightarrow 13x^2-9x^2=9+391 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
6. \(7x^2-684=10x^2-9 \\ \Leftrightarrow 7x^2-10x^2=-9+684 \\ \Leftrightarrow -3x^2 = 675 \\ \Leftrightarrow x^2 = \frac{675}{-3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5(6x^2-3)=-(-23x^2-832) \\ \Leftrightarrow 30x^2-15=23x^2+832 \\ \Leftrightarrow 30x^2-23x^2=832+15 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(7x^2-1008=0 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
9. \(-2x^2-58=-5x^2-10 \\ \Leftrightarrow -2x^2+5x^2=-10+58 \\ \Leftrightarrow 3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
10. \(-2x^2+338=0 \\ \Leftrightarrow -2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{-2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(-3x^2-243=0 \\ \Leftrightarrow -3x^2 = 243 \\ \Leftrightarrow x^2 = \frac{243}{-3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2(6x^2+2)=-(-7x^2-724) \\ \Leftrightarrow 12x^2+4=7x^2+724 \\ \Leftrightarrow 12x^2-7x^2=724-4 \\ \Leftrightarrow 5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)