Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+196=0\)
2. \(4x^2-4=0\)
3. \(7x^2-66=4x^2+9\)
4. \(-5(3x^2-5)=-(17x^2-225)\)
5. \(-x^2-5=-3x^2+3\)
6. \(x^2+10=3x^2+10\)
7. \(4(-6x^2+4)=-(29x^2+229)\)
8. \(5x^2+192=-3x^2-8\)
9. \(12x^2-597=7x^2+8\)
10. \(3x^2-432=0\)
11. \(4(9x^2+10)=-(-43x^2+23)\)
12. \(-4(4x^2-2)=-(15x^2-8)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+196=0 \\ \Leftrightarrow -4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(4x^2-4=0 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(7x^2-66=4x^2+9 \\ \Leftrightarrow 7x^2-4x^2=9+66 \\ \Leftrightarrow 3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(-5(3x^2-5)=-(17x^2-225) \\ \Leftrightarrow -15x^2+25=-17x^2+225 \\ \Leftrightarrow -15x^2+17x^2=225-25 \\ \Leftrightarrow 2x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{2}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(-x^2-5=-3x^2+3 \\ \Leftrightarrow -x^2+3x^2=3+5 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(x^2+10=3x^2+10 \\ \Leftrightarrow x^2-3x^2=10-10 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(4(-6x^2+4)=-(29x^2+229) \\ \Leftrightarrow -24x^2+16=-29x^2-229 \\ \Leftrightarrow -24x^2+29x^2=-229-16 \\ \Leftrightarrow 5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5x^2+192=-3x^2-8 \\ \Leftrightarrow 5x^2+3x^2=-8-192 \\ \Leftrightarrow 8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(12x^2-597=7x^2+8 \\ \Leftrightarrow 12x^2-7x^2=8+597 \\ \Leftrightarrow 5x^2 = 605 \\ \Leftrightarrow x^2 = \frac{605}{5}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(3x^2-432=0 \\ \Leftrightarrow 3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(4(9x^2+10)=-(-43x^2+23) \\ \Leftrightarrow 36x^2+40=43x^2-23 \\ \Leftrightarrow 36x^2-43x^2=-23-40 \\ \Leftrightarrow -7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{-7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
12. \(-4(4x^2-2)=-(15x^2-8) \\ \Leftrightarrow -16x^2+8=-15x^2+8 \\ \Leftrightarrow -16x^2+15x^2=8-8 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)