Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2+90=4x^2-8\)
2. \(-4x^2+0=0\)
3. \(-5x^2+720=0\)
4. \(2(-8x^2-6)=-(22x^2-1164)\)
5. \(-7x^2-187=-2x^2-7\)
6. \(-4x^2+256=0\)
7. \(-5x^2+180=0\)
8. \(2x^2+2=6x^2-2\)
9. \(4(10x^2+7)=-(-46x^2+1322)\)
10. \(-2(7x^2-8)=-(15x^2-16)\)
11. \(-5(8x^2-7)=-(46x^2-185)\)
12. \(-3(5x^2-8)=-(11x^2+300)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2+90=4x^2-8 \\ \Leftrightarrow 2x^2-4x^2=-8-90 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-5x^2+720=0 \\ \Leftrightarrow -5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{-5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
4. \(2(-8x^2-6)=-(22x^2-1164) \\ \Leftrightarrow -16x^2-12=-22x^2+1164 \\ \Leftrightarrow -16x^2+22x^2=1164+12 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
5. \(-7x^2-187=-2x^2-7 \\ \Leftrightarrow -7x^2+2x^2=-7+187 \\ \Leftrightarrow -5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4x^2+256=0 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(-5x^2+180=0 \\ \Leftrightarrow -5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{-5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
8. \(2x^2+2=6x^2-2 \\ \Leftrightarrow 2x^2-6x^2=-2-2 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(4(10x^2+7)=-(-46x^2+1322) \\ \Leftrightarrow 40x^2+28=46x^2-1322 \\ \Leftrightarrow 40x^2-46x^2=-1322-28 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(-2(7x^2-8)=-(15x^2-16) \\ \Leftrightarrow -14x^2+16=-15x^2+16 \\ \Leftrightarrow -14x^2+15x^2=16-16 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-5(8x^2-7)=-(46x^2-185) \\ \Leftrightarrow -40x^2+35=-46x^2+185 \\ \Leftrightarrow -40x^2+46x^2=185-35 \\ \Leftrightarrow 6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(-3(5x^2-8)=-(11x^2+300) \\ \Leftrightarrow -15x^2+24=-11x^2-300 \\ \Leftrightarrow -15x^2+11x^2=-300-24 \\ \Leftrightarrow -4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{-4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)