Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+784=0\)
2. \(-8x^2-392=0\)
3. \(-x^2+49=0\)
4. \(-2x^2+10=-5x^2-2\)
5. \(-6x^2+150=0\)
6. \(-4(-7x^2-7)=-(-32x^2+296)\)
7. \(3(-10x^2-9)=-(37x^2-1345)\)
8. \(-6x^2-332=-10x^2-8\)
9. \(5x^2+125=0\)
10. \(2(6x^2-6)=-(-20x^2-956)\)
11. \(3x^2-588=0\)
12. \(3x^2+675=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+784=0 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(-8x^2-392=0 \\ \Leftrightarrow -8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-x^2+49=0 \\ \Leftrightarrow -x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{-1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
4. \(-2x^2+10=-5x^2-2 \\ \Leftrightarrow -2x^2+5x^2=-2-10 \\ \Leftrightarrow 3x^2 = -12 \\ \Leftrightarrow x^2 = \frac{-12}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-6x^2+150=0 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(-4(-7x^2-7)=-(-32x^2+296) \\ \Leftrightarrow 28x^2+28=32x^2-296 \\ \Leftrightarrow 28x^2-32x^2=-296-28 \\ \Leftrightarrow -4x^2 = -324 \\ \Leftrightarrow x^2 = \frac{-324}{-4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(3(-10x^2-9)=-(37x^2-1345) \\ \Leftrightarrow -30x^2-27=-37x^2+1345 \\ \Leftrightarrow -30x^2+37x^2=1345+27 \\ \Leftrightarrow 7x^2 = 1372 \\ \Leftrightarrow x^2 = \frac{1372}{7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(-6x^2-332=-10x^2-8 \\ \Leftrightarrow -6x^2+10x^2=-8+332 \\ \Leftrightarrow 4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(5x^2+125=0 \\ \Leftrightarrow 5x^2 = -125 \\ \Leftrightarrow x^2 = \frac{-125}{5} < 0 \\ V = \varnothing \\ -----------------\)
10. \(2(6x^2-6)=-(-20x^2-956) \\ \Leftrightarrow 12x^2-12=20x^2+956 \\ \Leftrightarrow 12x^2-20x^2=956+12 \\ \Leftrightarrow -8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{-8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(3x^2-588=0 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(3x^2+675=0 \\ \Leftrightarrow 3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{3} < 0 \\ V = \varnothing \\ -----------------\)