Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(-10x^2+8)=-(-45x^2-940)\)
2. \(-3x^2+108=0\)
3. \(-7x^2+1183=0\)
4. \(6x^2-40=10x^2-4\)
5. \(-10x^2+6=-8x^2+6\)
6. \(-2(-2x^2+7)=-(x^2+19)\)
7. \(12x^2+672=9x^2-3\)
8. \(7x^2+252=0\)
9. \(-3x^2+5=5x^2+5\)
10. \(3(-4x^2+2)=-(19x^2+1)\)
11. \(-2(-10x^2+10)=-(-12x^2-12)\)
12. \(6x^2+153=8x^2-9\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(-10x^2+8)=-(-45x^2-940) \\ \Leftrightarrow 50x^2-40=45x^2+940 \\ \Leftrightarrow 50x^2-45x^2=940+40 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(-3x^2+108=0 \\ \Leftrightarrow -3x^2 = -108 \\ \Leftrightarrow x^2 = \frac{-108}{-3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(-7x^2+1183=0 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(6x^2-40=10x^2-4 \\ \Leftrightarrow 6x^2-10x^2=-4+40 \\ \Leftrightarrow -4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-4} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-10x^2+6=-8x^2+6 \\ \Leftrightarrow -10x^2+8x^2=6-6 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-2(-2x^2+7)=-(x^2+19) \\ \Leftrightarrow 4x^2-14=-x^2-19 \\ \Leftrightarrow 4x^2+x^2=-19+14 \\ \Leftrightarrow 5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(12x^2+672=9x^2-3 \\ \Leftrightarrow 12x^2-9x^2=-3-672 \\ \Leftrightarrow 3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{3} < 0 \\ V = \varnothing \\ -----------------\)
8. \(7x^2+252=0 \\ \Leftrightarrow 7x^2 = -252 \\ \Leftrightarrow x^2 = \frac{-252}{7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-3x^2+5=5x^2+5 \\ \Leftrightarrow -3x^2-5x^2=5-5 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(3(-4x^2+2)=-(19x^2+1) \\ \Leftrightarrow -12x^2+6=-19x^2-1 \\ \Leftrightarrow -12x^2+19x^2=-1-6 \\ \Leftrightarrow 7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-2(-10x^2+10)=-(-12x^2-12) \\ \Leftrightarrow 20x^2-20=12x^2+12 \\ \Leftrightarrow 20x^2-12x^2=12+20 \\ \Leftrightarrow 8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(6x^2+153=8x^2-9 \\ \Leftrightarrow 6x^2-8x^2=-9-153 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)