Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(10x^2-9)=-(46x^2-330)\)
2. \(2(-4x^2-6)=-(0x^2+524)\)
3. \(5(-6x^2+9)=-(26x^2-45)\)
4. \(-8x^2+200=0\)
5. \(-4(8x^2-6)=-(31x^2+12)\)
6. \(8x^2+11=10x^2+3\)
7. \(-7x^2-7=0\)
8. \(4(-6x^2-6)=-(22x^2-264)\)
9. \(-17x^2-443=-10x^2+5\)
10. \(x^2+81=0\)
11. \(x^2-100=4x^2+8\)
12. \(-3(-8x^2-3)=-(-29x^2+236)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(10x^2-9)=-(46x^2-330) \\ \Leftrightarrow -40x^2+36=-46x^2+330 \\ \Leftrightarrow -40x^2+46x^2=330-36 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(2(-4x^2-6)=-(0x^2+524) \\ \Leftrightarrow -8x^2-12=0x^2-524 \\ \Leftrightarrow -8x^2+0x^2=-524+12 \\ \Leftrightarrow -8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{-8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
3. \(5(-6x^2+9)=-(26x^2-45) \\ \Leftrightarrow -30x^2+45=-26x^2+45 \\ \Leftrightarrow -30x^2+26x^2=45-45 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-8x^2+200=0 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-4(8x^2-6)=-(31x^2+12) \\ \Leftrightarrow -32x^2+24=-31x^2-12 \\ \Leftrightarrow -32x^2+31x^2=-12-24 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
6. \(8x^2+11=10x^2+3 \\ \Leftrightarrow 8x^2-10x^2=3-11 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
7. \(-7x^2-7=0 \\ \Leftrightarrow -7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{-7} < 0 \\ V = \varnothing \\ -----------------\)
8. \(4(-6x^2-6)=-(22x^2-264) \\ \Leftrightarrow -24x^2-24=-22x^2+264 \\ \Leftrightarrow -24x^2+22x^2=264+24 \\ \Leftrightarrow -2x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-17x^2-443=-10x^2+5 \\ \Leftrightarrow -17x^2+10x^2=5+443 \\ \Leftrightarrow -7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{-7} < 0 \\ V = \varnothing \\ -----------------\)
10. \(x^2+81=0 \\ \Leftrightarrow x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{1} < 0 \\ V = \varnothing \\ -----------------\)
11. \(x^2-100=4x^2+8 \\ \Leftrightarrow x^2-4x^2=8+100 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-3(-8x^2-3)=-(-29x^2+236) \\ \Leftrightarrow 24x^2+9=29x^2-236 \\ \Leftrightarrow 24x^2-29x^2=-236-9 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)