Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(6x^2+3)=-(31x^2-34)\)
2. \(8x^2-512=0\)
3. \(-4(4x^2-3)=-(8x^2+1340)\)
4. \(-7x^2+1372=0\)
5. \(6x^2-294=0\)
6. \(x^2-81=0\)
7. \(-6x^2+294=0\)
8. \(-3x^2+726=2x^2+6\)
9. \(4(-2x^2-2)=-(7x^2+8)\)
10. \(2x^2+408=6x^2+8\)
11. \(5x^2-78=7x^2-6\)
12. \(-16x^2-49=-10x^2+5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(6x^2+3)=-(31x^2-34) \\ \Leftrightarrow -30x^2-15=-31x^2+34 \\ \Leftrightarrow -30x^2+31x^2=34+15 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(8x^2-512=0 \\ \Leftrightarrow 8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
3. \(-4(4x^2-3)=-(8x^2+1340) \\ \Leftrightarrow -16x^2+12=-8x^2-1340 \\ \Leftrightarrow -16x^2+8x^2=-1340-12 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(-7x^2+1372=0 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(6x^2-294=0 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(x^2-81=0 \\ \Leftrightarrow x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(-6x^2+294=0 \\ \Leftrightarrow -6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{-6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
8. \(-3x^2+726=2x^2+6 \\ \Leftrightarrow -3x^2-2x^2=6-726 \\ \Leftrightarrow -5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{-5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
9. \(4(-2x^2-2)=-(7x^2+8) \\ \Leftrightarrow -8x^2-8=-7x^2-8 \\ \Leftrightarrow -8x^2+7x^2=-8+8 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(2x^2+408=6x^2+8 \\ \Leftrightarrow 2x^2-6x^2=8-408 \\ \Leftrightarrow -4x^2 = -400 \\ \Leftrightarrow x^2 = \frac{-400}{-4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
11. \(5x^2-78=7x^2-6 \\ \Leftrightarrow 5x^2-7x^2=-6+78 \\ \Leftrightarrow -2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-16x^2-49=-10x^2+5 \\ \Leftrightarrow -16x^2+10x^2=5+49 \\ \Leftrightarrow -6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{-6} < 0 \\ V = \varnothing \\ -----------------\)