Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2+245=0\)
2. \(-9x^2-9=-7x^2+9\)
3. \(x^2-169=0\)
4. \(4x^2-36=0\)
5. \(-5(-6x^2-6)=-(-28x^2+212)\)
6. \(-3(-6x^2+7)=-(-19x^2+121)\)
7. \(-5(-7x^2+4)=-(-37x^2-52)\)
8. \(-2x^2+98=0\)
9. \(3(-6x^2-3)=-(21x^2+9)\)
10. \(-7x^2+7=0\)
11. \(2x^2+0=0\)
12. \(6x^2-1176=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2+245=0 \\ \Leftrightarrow -5x^2 = -245 \\ \Leftrightarrow x^2 = \frac{-245}{-5}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(-9x^2-9=-7x^2+9 \\ \Leftrightarrow -9x^2+7x^2=9+9 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)
3. \(x^2-169=0 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(4x^2-36=0 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
5. \(-5(-6x^2-6)=-(-28x^2+212) \\ \Leftrightarrow 30x^2+30=28x^2-212 \\ \Leftrightarrow 30x^2-28x^2=-212-30 \\ \Leftrightarrow 2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-3(-6x^2+7)=-(-19x^2+121) \\ \Leftrightarrow 18x^2-21=19x^2-121 \\ \Leftrightarrow 18x^2-19x^2=-121+21 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(-5(-7x^2+4)=-(-37x^2-52) \\ \Leftrightarrow 35x^2-20=37x^2+52 \\ \Leftrightarrow 35x^2-37x^2=52+20 \\ \Leftrightarrow -2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-2x^2+98=0 \\ \Leftrightarrow -2x^2 = -98 \\ \Leftrightarrow x^2 = \frac{-98}{-2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(3(-6x^2-3)=-(21x^2+9) \\ \Leftrightarrow -18x^2-9=-21x^2-9 \\ \Leftrightarrow -18x^2+21x^2=-9+9 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(-7x^2+7=0 \\ \Leftrightarrow -7x^2 = -7 \\ \Leftrightarrow x^2 = \frac{-7}{-7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
11. \(2x^2+0=0 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(6x^2-1176=0 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)