Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-5x^2+8)=-(9x^2+72)\)
2. \(-2(5x^2+7)=-(13x^2+14)\)
3. \(8x^2-1568=0\)
4. \(4(5x^2-7)=-(-22x^2+100)\)
5. \(-4(-9x^2+4)=-(-41x^2+261)\)
6. \(-7x^2+7=0\)
7. \(-2(-7x^2-4)=-(-6x^2-1808)\)
8. \(-5(-8x^2-6)=-(-33x^2+33)\)
9. \(-18x^2+977=-10x^2+9\)
10. \(4(10x^2-4)=-(-39x^2-33)\)
11. \(-8x^2+1352=0\)
12. \(3(-3x^2-6)=-(16x^2-1557)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-5x^2+8)=-(9x^2+72) \\ \Leftrightarrow -15x^2+24=-9x^2-72 \\ \Leftrightarrow -15x^2+9x^2=-72-24 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-2(5x^2+7)=-(13x^2+14) \\ \Leftrightarrow -10x^2-14=-13x^2-14 \\ \Leftrightarrow -10x^2+13x^2=-14+14 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(8x^2-1568=0 \\ \Leftrightarrow 8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(4(5x^2-7)=-(-22x^2+100) \\ \Leftrightarrow 20x^2-28=22x^2-100 \\ \Leftrightarrow 20x^2-22x^2=-100+28 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
5. \(-4(-9x^2+4)=-(-41x^2+261) \\ \Leftrightarrow 36x^2-16=41x^2-261 \\ \Leftrightarrow 36x^2-41x^2=-261+16 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(-7x^2+7=0 \\ \Leftrightarrow -7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{-7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(-2(-7x^2-4)=-(-6x^2-1808) \\ \Leftrightarrow 14x^2+8=6x^2+1808 \\ \Leftrightarrow 14x^2-6x^2=1808-8 \\ \Leftrightarrow 8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(-5(-8x^2-6)=-(-33x^2+33) \\ \Leftrightarrow 40x^2+30=33x^2-33 \\ \Leftrightarrow 40x^2-33x^2=-33-30 \\ \Leftrightarrow 7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-18x^2+977=-10x^2+9 \\ \Leftrightarrow -18x^2+10x^2=9-977 \\ \Leftrightarrow -8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{-8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(4(10x^2-4)=-(-39x^2-33) \\ \Leftrightarrow 40x^2-16=39x^2+33 \\ \Leftrightarrow 40x^2-39x^2=33+16 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(-8x^2+1352=0 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
12. \(3(-3x^2-6)=-(16x^2-1557) \\ \Leftrightarrow -9x^2-18=-16x^2+1557 \\ \Leftrightarrow -9x^2+16x^2=1557+18 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)