Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(-6x^2+4)=-(-22x^2-376)\)
2. \(-5x^2+980=0\)
3. \(-4(5x^2-10)=-(24x^2-296)\)
4. \(2x^2+338=0\)
5. \(-5x^2+125=0\)
6. \(-3(4x^2+5)=-(20x^2+15)\)
7. \(-7x^2+1183=0\)
8. \(2x^2+198=4x^2-2\)
9. \(-3(6x^2+4)=-(15x^2+600)\)
10. \(5(-3x^2-7)=-(23x^2+43)\)
11. \(-3(8x^2-2)=-(28x^2+250)\)
12. \(4(10x^2-6)=-(-32x^2+1376)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(-6x^2+4)=-(-22x^2-376) \\ \Leftrightarrow 24x^2-16=22x^2+376 \\ \Leftrightarrow 24x^2-22x^2=376+16 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(-5x^2+980=0 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(-4(5x^2-10)=-(24x^2-296) \\ \Leftrightarrow -20x^2+40=-24x^2+296 \\ \Leftrightarrow -20x^2+24x^2=296-40 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
4. \(2x^2+338=0 \\ \Leftrightarrow 2x^2 = -338 \\ \Leftrightarrow x^2 = \frac{-338}{2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-5x^2+125=0 \\ \Leftrightarrow -5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{-5}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(-3(4x^2+5)=-(20x^2+15) \\ \Leftrightarrow -12x^2-15=-20x^2-15 \\ \Leftrightarrow -12x^2+20x^2=-15+15 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-7x^2+1183=0 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(2x^2+198=4x^2-2 \\ \Leftrightarrow 2x^2-4x^2=-2-198 \\ \Leftrightarrow -2x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-2}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-3(6x^2+4)=-(15x^2+600) \\ \Leftrightarrow -18x^2-12=-15x^2-600 \\ \Leftrightarrow -18x^2+15x^2=-600+12 \\ \Leftrightarrow -3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{-3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(5(-3x^2-7)=-(23x^2+43) \\ \Leftrightarrow -15x^2-35=-23x^2-43 \\ \Leftrightarrow -15x^2+23x^2=-43+35 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-3(8x^2-2)=-(28x^2+250) \\ \Leftrightarrow -24x^2+6=-28x^2-250 \\ \Leftrightarrow -24x^2+28x^2=-250-6 \\ \Leftrightarrow 4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4(10x^2-6)=-(-32x^2+1376) \\ \Leftrightarrow 40x^2-24=32x^2-1376 \\ \Leftrightarrow 40x^2-32x^2=-1376+24 \\ \Leftrightarrow 8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{8} < 0 \\ V = \varnothing \\ -----------------\)