Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-13x^2+38=-5x^2+6\)
2. \(-5x^2+241=-2x^2-2\)
3. \(7x^2+448=0\)
4. \(-2x^2-186=-5x^2+6\)
5. \(-5(-10x^2+3)=-(-56x^2+69)\)
6. \(4(-7x^2+4)=-(31x^2-163)\)
7. \(-2(-2x^2+3)=-(-8x^2+22)\)
8. \(6x^2+726=0\)
9. \(x^2-582=4x^2+6\)
10. \(-3x^2+507=0\)
11. \(-3(10x^2+6)=-(23x^2-549)\)
12. \(-14x^2+686=-10x^2+10\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-13x^2+38=-5x^2+6 \\ \Leftrightarrow -13x^2+5x^2=6-38 \\ \Leftrightarrow -8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(-5x^2+241=-2x^2-2 \\ \Leftrightarrow -5x^2+2x^2=-2-241 \\ \Leftrightarrow -3x^2 = -243 \\ \Leftrightarrow x^2 = \frac{-243}{-3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
3. \(7x^2+448=0 \\ \Leftrightarrow 7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2x^2-186=-5x^2+6 \\ \Leftrightarrow -2x^2+5x^2=6+186 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(-5(-10x^2+3)=-(-56x^2+69) \\ \Leftrightarrow 50x^2-15=56x^2-69 \\ \Leftrightarrow 50x^2-56x^2=-69+15 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
6. \(4(-7x^2+4)=-(31x^2-163) \\ \Leftrightarrow -28x^2+16=-31x^2+163 \\ \Leftrightarrow -28x^2+31x^2=163-16 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-2(-2x^2+3)=-(-8x^2+22) \\ \Leftrightarrow 4x^2-6=8x^2-22 \\ \Leftrightarrow 4x^2-8x^2=-22+6 \\ \Leftrightarrow -4x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{-4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
8. \(6x^2+726=0 \\ \Leftrightarrow 6x^2 = -726 \\ \Leftrightarrow x^2 = \frac{-726}{6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(x^2-582=4x^2+6 \\ \Leftrightarrow x^2-4x^2=6+582 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-3x^2+507=0 \\ \Leftrightarrow -3x^2 = -507 \\ \Leftrightarrow x^2 = \frac{-507}{-3}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(-3(10x^2+6)=-(23x^2-549) \\ \Leftrightarrow -30x^2-18=-23x^2+549 \\ \Leftrightarrow -30x^2+23x^2=549+18 \\ \Leftrightarrow -7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{-7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-14x^2+686=-10x^2+10 \\ \Leftrightarrow -14x^2+10x^2=10-686 \\ \Leftrightarrow -4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{-4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)