Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2+0=0\)
2. \(-2(5x^2+6)=-(12x^2+84)\)
3. \(2(-8x^2-5)=-(13x^2-233)\)
4. \(-2x^2+6=6x^2-2\)
5. \(-15x^2+1791=-7x^2-9\)
6. \(-5(6x^2-6)=-(34x^2-30)\)
7. \(4(2x^2+9)=-(-12x^2-180)\)
8. \(x^2+42=5x^2+6\)
9. \(-6x^2+486=0\)
10. \(-6x^2+280=2x^2-8\)
11. \(-5x^2-720=0\)
12. \(8x^2-8=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2+0=0 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-2(5x^2+6)=-(12x^2+84) \\ \Leftrightarrow -10x^2-12=-12x^2-84 \\ \Leftrightarrow -10x^2+12x^2=-84+12 \\ \Leftrightarrow 2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2(-8x^2-5)=-(13x^2-233) \\ \Leftrightarrow -16x^2-10=-13x^2+233 \\ \Leftrightarrow -16x^2+13x^2=233+10 \\ \Leftrightarrow -3x^2 = 243 \\ \Leftrightarrow x^2 = \frac{243}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2x^2+6=6x^2-2 \\ \Leftrightarrow -2x^2-6x^2=-2-6 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-15x^2+1791=-7x^2-9 \\ \Leftrightarrow -15x^2+7x^2=-9-1791 \\ \Leftrightarrow -8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
6. \(-5(6x^2-6)=-(34x^2-30) \\ \Leftrightarrow -30x^2+30=-34x^2+30 \\ \Leftrightarrow -30x^2+34x^2=30-30 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(4(2x^2+9)=-(-12x^2-180) \\ \Leftrightarrow 8x^2+36=12x^2+180 \\ \Leftrightarrow 8x^2-12x^2=180-36 \\ \Leftrightarrow -4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{-4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(x^2+42=5x^2+6 \\ \Leftrightarrow x^2-5x^2=6-42 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-6x^2+486=0 \\ \Leftrightarrow -6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{-6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(-6x^2+280=2x^2-8 \\ \Leftrightarrow -6x^2-2x^2=-8-280 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(-5x^2-720=0 \\ \Leftrightarrow -5x^2 = 720 \\ \Leftrightarrow x^2 = \frac{720}{-5} < 0 \\ V = \varnothing \\ -----------------\)
12. \(8x^2-8=0 \\ \Leftrightarrow 8x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)