Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-1152=0\)
2. \(8x^2-392=0\)
3. \(-13x^2-8=-10x^2-8\)
4. \(-2(6x^2-9)=-(9x^2+414)\)
5. \(-13x^2-593=-10x^2-5\)
6. \(-8x^2+668=-5x^2-7\)
7. \(-6x^2-230=-7x^2-5\)
8. \(18x^2-970=10x^2-2\)
9. \(-4x^2+4=-9x^2+9\)
10. \(-4(-6x^2+6)=-(-32x^2-1328)\)
11. \(7x^2+7=0\)
12. \(2(-10x^2-6)=-(24x^2-132)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-1152=0 \\ \Leftrightarrow -8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{-8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(8x^2-392=0 \\ \Leftrightarrow 8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(-13x^2-8=-10x^2-8 \\ \Leftrightarrow -13x^2+10x^2=-8+8 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-2(6x^2-9)=-(9x^2+414) \\ \Leftrightarrow -12x^2+18=-9x^2-414 \\ \Leftrightarrow -12x^2+9x^2=-414-18 \\ \Leftrightarrow -3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{-3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
5. \(-13x^2-593=-10x^2-5 \\ \Leftrightarrow -13x^2+10x^2=-5+593 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-8x^2+668=-5x^2-7 \\ \Leftrightarrow -8x^2+5x^2=-7-668 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(-6x^2-230=-7x^2-5 \\ \Leftrightarrow -6x^2+7x^2=-5+230 \\ \Leftrightarrow x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{1}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(18x^2-970=10x^2-2 \\ \Leftrightarrow 18x^2-10x^2=-2+970 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-4x^2+4=-9x^2+9 \\ \Leftrightarrow -4x^2+9x^2=9-4 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
10. \(-4(-6x^2+6)=-(-32x^2-1328) \\ \Leftrightarrow 24x^2-24=32x^2+1328 \\ \Leftrightarrow 24x^2-32x^2=1328+24 \\ \Leftrightarrow -8x^2 = 1352 \\ \Leftrightarrow x^2 = \frac{1352}{-8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(7x^2+7=0 \\ \Leftrightarrow 7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(2(-10x^2-6)=-(24x^2-132) \\ \Leftrightarrow -20x^2-12=-24x^2+132 \\ \Leftrightarrow -20x^2+24x^2=132+12 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)