Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2+977=9x^2+9\)
2. \(2(-8x^2+8)=-(11x^2-96)\)
3. \(3(-4x^2+4)=-(19x^2-579)\)
4. \(3(-3x^2+7)=-(14x^2+1104)\)
5. \(-11x^2+593=-8x^2+5\)
6. \(4x^2-144=0\)
7. \(2(-10x^2+3)=-(26x^2-1182)\)
8. \(2x^2-338=0\)
9. \(-12x^2-4=-8x^2-4\)
10. \(8x^2+281=6x^2-7\)
11. \(-4(-3x^2-3)=-(-19x^2+1360)\)
12. \(3(10x^2+8)=-(-25x^2-24)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2+977=9x^2+9 \\ \Leftrightarrow x^2-9x^2=9-977 \\ \Leftrightarrow -8x^2 = -968 \\ \Leftrightarrow x^2 = \frac{-968}{-8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
2. \(2(-8x^2+8)=-(11x^2-96) \\ \Leftrightarrow -16x^2+16=-11x^2+96 \\ \Leftrightarrow -16x^2+11x^2=96-16 \\ \Leftrightarrow -5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{-5} < 0 \\ V = \varnothing \\ -----------------\)
3. \(3(-4x^2+4)=-(19x^2-579) \\ \Leftrightarrow -12x^2+12=-19x^2+579 \\ \Leftrightarrow -12x^2+19x^2=579-12 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(3(-3x^2+7)=-(14x^2+1104) \\ \Leftrightarrow -9x^2+21=-14x^2-1104 \\ \Leftrightarrow -9x^2+14x^2=-1104-21 \\ \Leftrightarrow 5x^2 = -1125 \\ \Leftrightarrow x^2 = \frac{-1125}{5} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-11x^2+593=-8x^2+5 \\ \Leftrightarrow -11x^2+8x^2=5-593 \\ \Leftrightarrow -3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{-3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(4x^2-144=0 \\ \Leftrightarrow 4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{4}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
7. \(2(-10x^2+3)=-(26x^2-1182) \\ \Leftrightarrow -20x^2+6=-26x^2+1182 \\ \Leftrightarrow -20x^2+26x^2=1182-6 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(2x^2-338=0 \\ \Leftrightarrow 2x^2 = 338 \\ \Leftrightarrow x^2 = \frac{338}{2}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-12x^2-4=-8x^2-4 \\ \Leftrightarrow -12x^2+8x^2=-4+4 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(8x^2+281=6x^2-7 \\ \Leftrightarrow 8x^2-6x^2=-7-281 \\ \Leftrightarrow 2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{2} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-4(-3x^2-3)=-(-19x^2+1360) \\ \Leftrightarrow 12x^2+12=19x^2-1360 \\ \Leftrightarrow 12x^2-19x^2=-1360-12 \\ \Leftrightarrow -7x^2 = -1372 \\ \Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(3(10x^2+8)=-(-25x^2-24) \\ \Leftrightarrow 30x^2+24=25x^2+24 \\ \Leftrightarrow 30x^2-25x^2=24-24 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)