Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2+0=0\)
2. \(x^2-49=0\)
3. \(-5(-8x^2-3)=-(-43x^2-207)\)
4. \(2(6x^2-8)=-(-14x^2+258)\)
5. \(-6x^2+6=0\)
6. \(-2(7x^2-5)=-(16x^2-12)\)
7. \(x^2+91=7x^2-5\)
8. \(-5(-3x^2-5)=-(-23x^2-673)\)
9. \(-7x^2-334=-9x^2+4\)
10. \(-2x^2-4=5x^2-4\)
11. \(6x^2+384=0\)
12. \(-8x^2+1800=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2+0=0 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(x^2-49=0 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(-5(-8x^2-3)=-(-43x^2-207) \\ \Leftrightarrow 40x^2+15=43x^2+207 \\ \Leftrightarrow 40x^2-43x^2=207-15 \\ \Leftrightarrow -3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(2(6x^2-8)=-(-14x^2+258) \\ \Leftrightarrow 12x^2-16=14x^2-258 \\ \Leftrightarrow 12x^2-14x^2=-258+16 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
5. \(-6x^2+6=0 \\ \Leftrightarrow -6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{-6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(-2(7x^2-5)=-(16x^2-12) \\ \Leftrightarrow -14x^2+10=-16x^2+12 \\ \Leftrightarrow -14x^2+16x^2=12-10 \\ \Leftrightarrow 2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(x^2+91=7x^2-5 \\ \Leftrightarrow x^2-7x^2=-5-91 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-5(-3x^2-5)=-(-23x^2-673) \\ \Leftrightarrow 15x^2+25=23x^2+673 \\ \Leftrightarrow 15x^2-23x^2=673-25 \\ \Leftrightarrow -8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{-8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-7x^2-334=-9x^2+4 \\ \Leftrightarrow -7x^2+9x^2=4+334 \\ \Leftrightarrow 2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(-2x^2-4=5x^2-4 \\ \Leftrightarrow -2x^2-5x^2=-4+4 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(6x^2+384=0 \\ \Leftrightarrow 6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-8x^2+1800=0 \\ \Leftrightarrow -8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)