Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(4x^2+4)=-(-10x^2-742)\)
2. \(-3(5x^2+8)=-(18x^2+51)\)
3. \(x^2-16=0\)
4. \(5x^2+80=0\)
5. \(-3(4x^2-4)=-(11x^2-12)\)
6. \(x^2-81=0\)
7. \(10x^2-1567=3x^2+8\)
8. \(-3x^2-75=0\)
9. \(-4(6x^2-3)=-(29x^2-12)\)
10. \(x^2-1119=6x^2+6\)
11. \(15x^2-298=7x^2-10\)
12. \(3x^2+6=6x^2+6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(4x^2+4)=-(-10x^2-742) \\ \Leftrightarrow 16x^2+16=10x^2+742 \\ \Leftrightarrow 16x^2-10x^2=742-16 \\ \Leftrightarrow 6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(-3(5x^2+8)=-(18x^2+51) \\ \Leftrightarrow -15x^2-24=-18x^2-51 \\ \Leftrightarrow -15x^2+18x^2=-51+24 \\ \Leftrightarrow 3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(x^2-16=0 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(5x^2+80=0 \\ \Leftrightarrow 5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(4x^2-4)=-(11x^2-12) \\ \Leftrightarrow -12x^2+12=-11x^2+12 \\ \Leftrightarrow -12x^2+11x^2=12-12 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(x^2-81=0 \\ \Leftrightarrow x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(10x^2-1567=3x^2+8 \\ \Leftrightarrow 10x^2-3x^2=8+1567 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(-3x^2-75=0 \\ \Leftrightarrow -3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-4(6x^2-3)=-(29x^2-12) \\ \Leftrightarrow -24x^2+12=-29x^2+12 \\ \Leftrightarrow -24x^2+29x^2=12-12 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(x^2-1119=6x^2+6 \\ \Leftrightarrow x^2-6x^2=6+1119 \\ \Leftrightarrow -5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{-5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(15x^2-298=7x^2-10 \\ \Leftrightarrow 15x^2-7x^2=-10+298 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(3x^2+6=6x^2+6 \\ \Leftrightarrow 3x^2-6x^2=6-6 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)