Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(6x^2+8)=-(-5x^2-583)\)
2. \(x^2+9=0\)
3. \(6x^2-96=0\)
4. \(3(4x^2+7)=-(-19x^2+154)\)
5. \(6x^2-172=5x^2-3\)
6. \(2(6x^2-10)=-(-10x^2+38)\)
7. \(-5x^2+405=0\)
8. \(2x^2+128=0\)
9. \(4(7x^2+7)=-(-27x^2-37)\)
10. \(7x^2-26=5x^2-8\)
11. \(2x^2+50=0\)
12. \(2(6x^2-3)=-(-17x^2-14)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(6x^2+8)=-(-5x^2-583) \\ \Leftrightarrow 12x^2+16=5x^2+583 \\ \Leftrightarrow 12x^2-5x^2=583-16 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(x^2+9=0 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(6x^2-96=0 \\ \Leftrightarrow 6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(3(4x^2+7)=-(-19x^2+154) \\ \Leftrightarrow 12x^2+21=19x^2-154 \\ \Leftrightarrow 12x^2-19x^2=-154-21 \\ \Leftrightarrow -7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{-7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(6x^2-172=5x^2-3 \\ \Leftrightarrow 6x^2-5x^2=-3+172 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(2(6x^2-10)=-(-10x^2+38) \\ \Leftrightarrow 12x^2-20=10x^2-38 \\ \Leftrightarrow 12x^2-10x^2=-38+20 \\ \Leftrightarrow 2x^2 = -18 \\ \Leftrightarrow x^2 = \frac{-18}{2} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-5x^2+405=0 \\ \Leftrightarrow -5x^2 = -405 \\ \Leftrightarrow x^2 = \frac{-405}{-5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(2x^2+128=0 \\ \Leftrightarrow 2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{2} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4(7x^2+7)=-(-27x^2-37) \\ \Leftrightarrow 28x^2+28=27x^2+37 \\ \Leftrightarrow 28x^2-27x^2=37-28 \\ \Leftrightarrow x^2 = 9 \\ \Leftrightarrow x^2 = \frac{9}{1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(7x^2-26=5x^2-8 \\ \Leftrightarrow 7x^2-5x^2=-8+26 \\ \Leftrightarrow 2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{2}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(2x^2+50=0 \\ \Leftrightarrow 2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2(6x^2-3)=-(-17x^2-14) \\ \Leftrightarrow 12x^2-6=17x^2+14 \\ \Leftrightarrow 12x^2-17x^2=14+6 \\ \Leftrightarrow -5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{-5} < 0 \\ V = \varnothing \\ -----------------\)