Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(3x^2-8)=-(18x^2-416)\)
2. \(-7x^2+252=0\)
3. \(-3(3x^2+3)=-(7x^2+59)\)
4. \(-3(10x^2-4)=-(32x^2+6)\)
5. \(2x^2-1173=8x^2+3\)
6. \(x^2+16=0\)
7. \(12x^2-11=10x^2-3\)
8. \(-12x^2+1576=-4x^2+8\)
9. \(3(-5x^2-9)=-(19x^2+11)\)
10. \(-2x^2+0=0\)
11. \(-3(5x^2+3)=-(19x^2-247)\)
12. \(-7x^2+0=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(3x^2-8)=-(18x^2-416) \\ \Leftrightarrow -12x^2+32=-18x^2+416 \\ \Leftrightarrow -12x^2+18x^2=416-32 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
2. \(-7x^2+252=0 \\ \Leftrightarrow -7x^2 = -252 \\ \Leftrightarrow x^2 = \frac{-252}{-7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(-3(3x^2+3)=-(7x^2+59) \\ \Leftrightarrow -9x^2-9=-7x^2-59 \\ \Leftrightarrow -9x^2+7x^2=-59+9 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(-3(10x^2-4)=-(32x^2+6) \\ \Leftrightarrow -30x^2+12=-32x^2-6 \\ \Leftrightarrow -30x^2+32x^2=-6-12 \\ \Leftrightarrow 2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2x^2-1173=8x^2+3 \\ \Leftrightarrow 2x^2-8x^2=3+1173 \\ \Leftrightarrow -6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{-6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(x^2+16=0 \\ \Leftrightarrow x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(12x^2-11=10x^2-3 \\ \Leftrightarrow 12x^2-10x^2=-3+11 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(-12x^2+1576=-4x^2+8 \\ \Leftrightarrow -12x^2+4x^2=8-1576 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(3(-5x^2-9)=-(19x^2+11) \\ \Leftrightarrow -15x^2-27=-19x^2-11 \\ \Leftrightarrow -15x^2+19x^2=-11+27 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-2x^2+0=0 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-3(5x^2+3)=-(19x^2-247) \\ \Leftrightarrow -15x^2-9=-19x^2+247 \\ \Leftrightarrow -15x^2+19x^2=247+9 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(-7x^2+0=0 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)