Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+0=0\)
2. \(-8x^2+392=0\)
3. \(x^2+0=0\)
4. \(3(-10x^2-4)=-(33x^2+12)\)
5. \(2(10x^2+9)=-(-17x^2-21)\)
6. \(7x^2-700=0\)
7. \(-6x^2+1176=0\)
8. \(-2x^2+32=0\)
9. \(x^2+247=3x^2+5\)
10. \(2(-5x^2+8)=-(6x^2+560)\)
11. \(x^2+1020=-5x^2+6\)
12. \(-4(7x^2-2)=-(32x^2-152)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+0=0 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
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. \(x^2+0=0 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(3(-10x^2-4)=-(33x^2+12) \\ \Leftrightarrow -30x^2-12=-33x^2-12 \\ \Leftrightarrow -30x^2+33x^2=-12+12 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(2(10x^2+9)=-(-17x^2-21) \\ \Leftrightarrow 20x^2+18=17x^2+21 \\ \Leftrightarrow 20x^2-17x^2=21-18 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(7x^2-700=0 \\ \Leftrightarrow 7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(-6x^2+1176=0 \\ \Leftrightarrow -6x^2 = -1176 \\ \Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(-2x^2+32=0 \\ \Leftrightarrow -2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
9. \(x^2+247=3x^2+5 \\ \Leftrightarrow x^2-3x^2=5-247 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(2(-5x^2+8)=-(6x^2+560) \\ \Leftrightarrow -10x^2+16=-6x^2-560 \\ \Leftrightarrow -10x^2+6x^2=-560-16 \\ \Leftrightarrow -4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{-4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(x^2+1020=-5x^2+6 \\ \Leftrightarrow x^2+5x^2=6-1020 \\ \Leftrightarrow 6x^2 = -1014 \\ \Leftrightarrow x^2 = \frac{-1014}{6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-4(7x^2-2)=-(32x^2-152) \\ \Leftrightarrow -28x^2+8=-32x^2+152 \\ \Leftrightarrow -28x^2+32x^2=152-8 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)