Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2-225=0\)
2. \(2x^2+242=0\)
3. \(4(6x^2-5)=-(-26x^2-318)\)
4. \(14x^2-1348=8x^2+2\)
5. \(-10x^2-679=-7x^2-4\)
6. \(3(-7x^2-7)=-(17x^2+805)\)
7. \(3(-2x^2-9)=-(9x^2+27)\)
8. \(-17x^2+1577=-9x^2+9\)
9. \(6x^2-2=4x^2-2\)
10. \(x^2-1157=-7x^2-5\)
11. \(-8x^2-968=0\)
12. \(-7x^2+157=-4x^2+10\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2-225=0 \\ \Leftrightarrow -x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{-1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(2x^2+242=0 \\ \Leftrightarrow 2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(4(6x^2-5)=-(-26x^2-318) \\ \Leftrightarrow 24x^2-20=26x^2+318 \\ \Leftrightarrow 24x^2-26x^2=318+20 \\ \Leftrightarrow -2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{-2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(14x^2-1348=8x^2+2 \\ \Leftrightarrow 14x^2-8x^2=2+1348 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(-10x^2-679=-7x^2-4 \\ \Leftrightarrow -10x^2+7x^2=-4+679 \\ \Leftrightarrow -3x^2 = 675 \\ \Leftrightarrow x^2 = \frac{675}{-3} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3(-7x^2-7)=-(17x^2+805) \\ \Leftrightarrow -21x^2-21=-17x^2-805 \\ \Leftrightarrow -21x^2+17x^2=-805+21 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(3(-2x^2-9)=-(9x^2+27) \\ \Leftrightarrow -6x^2-27=-9x^2-27 \\ \Leftrightarrow -6x^2+9x^2=-27+27 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-17x^2+1577=-9x^2+9 \\ \Leftrightarrow -17x^2+9x^2=9-1577 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(6x^2-2=4x^2-2 \\ \Leftrightarrow 6x^2-4x^2=-2+2 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(x^2-1157=-7x^2-5 \\ \Leftrightarrow x^2+7x^2=-5+1157 \\ \Leftrightarrow 8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(-8x^2-968=0 \\ \Leftrightarrow -8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{-8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-7x^2+157=-4x^2+10 \\ \Leftrightarrow -7x^2+4x^2=10-157 \\ \Leftrightarrow -3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{-3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)