Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+702=8x^2+2\)
2. \(x^2-144=0\)
3. \(-6x^2+150=0\)
4. \(6x^2+0=0\)
5. \(2(10x^2+5)=-(-24x^2+90)\)
6. \(10x^2-442=8x^2+8\)
7. \(5(10x^2-9)=-(-54x^2+445)\)
8. \(-10x^2-349=-3x^2-6\)
9. \(-3x^2-9=-4x^2-9\)
10. \(3x^2-840=8x^2+5\)
11. \(6x^2-216=0\)
12. \(5x^2-1125=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+702=8x^2+2 \\ \Leftrightarrow x^2-8x^2=2-702 \\ \Leftrightarrow -7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{-7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(x^2-144=0 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(-6x^2+150=0 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(6x^2+0=0 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(2(10x^2+5)=-(-24x^2+90) \\ \Leftrightarrow 20x^2+10=24x^2-90 \\ \Leftrightarrow 20x^2-24x^2=-90-10 \\ \Leftrightarrow -4x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(10x^2-442=8x^2+8 \\ \Leftrightarrow 10x^2-8x^2=8+442 \\ \Leftrightarrow 2x^2 = 450 \\ \Leftrightarrow x^2 = \frac{450}{2}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(5(10x^2-9)=-(-54x^2+445) \\ \Leftrightarrow 50x^2-45=54x^2-445 \\ \Leftrightarrow 50x^2-54x^2=-445+45 \\ \Leftrightarrow -4x^2 = -400 \\ \Leftrightarrow x^2 = \frac{-400}{-4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(-10x^2-349=-3x^2-6 \\ \Leftrightarrow -10x^2+3x^2=-6+349 \\ \Leftrightarrow -7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{-7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-3x^2-9=-4x^2-9 \\ \Leftrightarrow -3x^2+4x^2=-9+9 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(3x^2-840=8x^2+5 \\ \Leftrightarrow 3x^2-8x^2=5+840 \\ \Leftrightarrow -5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{-5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(6x^2-216=0 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(5x^2-1125=0 \\ \Leftrightarrow 5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)