Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-10x^2+159=-8x^2-3\)
2. \(-2(-6x^2-10)=-(-11x^2+29)\)
3. \(-15x^2-68=-7x^2+4\)
4. \(-7x^2-48=-2x^2-3\)
5. \(-4x^2-676=0\)
6. \(-3x^2+432=0\)
7. \(7x^2-1008=0\)
8. \(-5(-10x^2-4)=-(-53x^2-20)\)
9. \(-15x^2+10=-9x^2+10\)
10. \(x^2+0=0\)
11. \(4x^2-144=0\)
12. \(-2(8x^2-8)=-(11x^2+29)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-10x^2+159=-8x^2-3 \\ \Leftrightarrow -10x^2+8x^2=-3-159 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(-2(-6x^2-10)=-(-11x^2+29) \\ \Leftrightarrow 12x^2+20=11x^2-29 \\ \Leftrightarrow 12x^2-11x^2=-29-20 \\ \Leftrightarrow x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-15x^2-68=-7x^2+4 \\ \Leftrightarrow -15x^2+7x^2=4+68 \\ \Leftrightarrow -8x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-7x^2-48=-2x^2-3 \\ \Leftrightarrow -7x^2+2x^2=-3+48 \\ \Leftrightarrow -5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{-5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-4x^2-676=0 \\ \Leftrightarrow -4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{-4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-3x^2+432=0 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
7. \(7x^2-1008=0 \\ \Leftrightarrow 7x^2 = 1008 \\ \Leftrightarrow x^2 = \frac{1008}{7}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
8. \(-5(-10x^2-4)=-(-53x^2-20) \\ \Leftrightarrow 50x^2+20=53x^2+20 \\ \Leftrightarrow 50x^2-53x^2=20-20 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-15x^2+10=-9x^2+10 \\ \Leftrightarrow -15x^2+9x^2=10-10 \\ \Leftrightarrow -6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(x^2+0=0 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(4x^2-144=0 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
12. \(-2(8x^2-8)=-(11x^2+29) \\ \Leftrightarrow -16x^2+16=-11x^2-29 \\ \Leftrightarrow -16x^2+11x^2=-29-16 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)