Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4(-6x^2-4)=-(-32x^2+1136)\)
2. \(-4(-2x^2-2)=-(-11x^2+19)\)
3. \(-2(9x^2-10)=-(16x^2-20)\)
4. \(-4x^2+256=0\)
5. \(-7x^2-1183=0\)
6. \(-3x^2-615=-8x^2-10\)
7. \(-15x^2-7=-8x^2-7\)
8. \(9x^2+47=8x^2-2\)
9. \(-2x^2+242=0\)
10. \(-3(-7x^2+3)=-(-19x^2-23)\)
11. \(-5x^2+0=0\)
12. \(-3(-7x^2+8)=-(-27x^2-1152)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4(-6x^2-4)=-(-32x^2+1136) \\ \Leftrightarrow 24x^2+16=32x^2-1136 \\ \Leftrightarrow 24x^2-32x^2=-1136-16 \\ \Leftrightarrow -8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{-8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
2. \(-4(-2x^2-2)=-(-11x^2+19) \\ \Leftrightarrow 8x^2+8=11x^2-19 \\ \Leftrightarrow 8x^2-11x^2=-19-8 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(-2(9x^2-10)=-(16x^2-20) \\ \Leftrightarrow -18x^2+20=-16x^2+20 \\ \Leftrightarrow -18x^2+16x^2=20-20 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-4x^2+256=0 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(-7x^2-1183=0 \\ \Leftrightarrow -7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{-7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-3x^2-615=-8x^2-10 \\ \Leftrightarrow -3x^2+8x^2=-10+615 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
7. \(-15x^2-7=-8x^2-7 \\ \Leftrightarrow -15x^2+8x^2=-7+7 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(9x^2+47=8x^2-2 \\ \Leftrightarrow 9x^2-8x^2=-2-47 \\ \Leftrightarrow x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{1} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-2x^2+242=0 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(-3(-7x^2+3)=-(-19x^2-23) \\ \Leftrightarrow 21x^2-9=19x^2+23 \\ \Leftrightarrow 21x^2-19x^2=23+9 \\ \Leftrightarrow 2x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-5x^2+0=0 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-3(-7x^2+8)=-(-27x^2-1152) \\ \Leftrightarrow 21x^2-24=27x^2+1152 \\ \Leftrightarrow 21x^2-27x^2=1152+24 \\ \Leftrightarrow -6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{-6} < 0 \\ V = \varnothing \\ -----------------\)