Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2-845=0\)
2. \(3(2x^2+3)=-(-14x^2-809)\)
3. \(-12x^2+3=-5x^2+3\)
4. \(7x^2+6=9x^2+4\)
5. \(-7x^2-343=0\)
6. \(-4(-2x^2+10)=-(-5x^2-260)\)
7. \(10x^2-366=7x^2-3\)
8. \(-9x^2+977=-4x^2-3\)
9. \(12x^2+7=9x^2+7\)
10. \(3(2x^2-4)=-(-x^2+992)\)
11. \(-3(4x^2-3)=-(17x^2-9)\)
12. \(-3(8x^2+6)=-(18x^2-582)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2-845=0 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
2. \(3(2x^2+3)=-(-14x^2-809) \\ \Leftrightarrow 6x^2+9=14x^2+809 \\ \Leftrightarrow 6x^2-14x^2=809-9 \\ \Leftrightarrow -8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{-8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-12x^2+3=-5x^2+3 \\ \Leftrightarrow -12x^2+5x^2=3-3 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(7x^2+6=9x^2+4 \\ \Leftrightarrow 7x^2-9x^2=4-6 \\ \Leftrightarrow -2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{-2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-7x^2-343=0 \\ \Leftrightarrow -7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{-7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4(-2x^2+10)=-(-5x^2-260) \\ \Leftrightarrow 8x^2-40=5x^2+260 \\ \Leftrightarrow 8x^2-5x^2=260+40 \\ \Leftrightarrow 3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(10x^2-366=7x^2-3 \\ \Leftrightarrow 10x^2-7x^2=-3+366 \\ \Leftrightarrow 3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{3}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(-9x^2+977=-4x^2-3 \\ \Leftrightarrow -9x^2+4x^2=-3-977 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(12x^2+7=9x^2+7 \\ \Leftrightarrow 12x^2-9x^2=7-7 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(3(2x^2-4)=-(-x^2+992) \\ \Leftrightarrow 6x^2-12=x^2-992 \\ \Leftrightarrow 6x^2-x^2=-992+12 \\ \Leftrightarrow 5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-3(4x^2-3)=-(17x^2-9) \\ \Leftrightarrow -12x^2+9=-17x^2+9 \\ \Leftrightarrow -12x^2+17x^2=9-9 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-3(8x^2+6)=-(18x^2-582) \\ \Leftrightarrow -24x^2-18=-18x^2+582 \\ \Leftrightarrow -24x^2+18x^2=582+18 \\ \Leftrightarrow -6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{-6} < 0 \\ V = \varnothing \\ -----------------\)