Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3(-7x^2+7)=-(24x^2-453)\)
2. \(4x^2-3=6x^2-3\)
3. \(-7x^2+7=0\)
4. \(-8x^2+0=0\)
5. \(-5(10x^2+4)=-(46x^2+20)\)
6. \(-5x^2-153=-4x^2-9\)
7. \(-4(-6x^2+9)=-(-19x^2-284)\)
8. \(x^2-36=0\)
9. \(-3x^2-3=2x^2-3\)
10. \(-6x^2+390=-4x^2-2\)
11. \(16x^2+110=9x^2-2\)
12. \(17x^2-6=9x^2+2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3(-7x^2+7)=-(24x^2-453) \\ \Leftrightarrow -21x^2+21=-24x^2+453 \\ \Leftrightarrow -21x^2+24x^2=453-21 \\ \Leftrightarrow 3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
2. \(4x^2-3=6x^2-3 \\ \Leftrightarrow 4x^2-6x^2=-3+3 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-7x^2+7=0 \\ \Leftrightarrow -7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{-7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(-8x^2+0=0 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-5(10x^2+4)=-(46x^2+20) \\ \Leftrightarrow -50x^2-20=-46x^2-20 \\ \Leftrightarrow -50x^2+46x^2=-20+20 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-5x^2-153=-4x^2-9 \\ \Leftrightarrow -5x^2+4x^2=-9+153 \\ \Leftrightarrow -x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-4(-6x^2+9)=-(-19x^2-284) \\ \Leftrightarrow 24x^2-36=19x^2+284 \\ \Leftrightarrow 24x^2-19x^2=284+36 \\ \Leftrightarrow 5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(x^2-36=0 \\ \Leftrightarrow x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
9. \(-3x^2-3=2x^2-3 \\ \Leftrightarrow -3x^2-2x^2=-3+3 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-6x^2+390=-4x^2-2 \\ \Leftrightarrow -6x^2+4x^2=-2-390 \\ \Leftrightarrow -2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{-2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(16x^2+110=9x^2-2 \\ \Leftrightarrow 16x^2-9x^2=-2-110 \\ \Leftrightarrow 7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(17x^2-6=9x^2+2 \\ \Leftrightarrow 17x^2-9x^2=2+6 \\ \Leftrightarrow 8x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)