Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2-864=0\)
2. \(-5(4x^2-6)=-(19x^2+139)\)
3. \(-4x^2+4=0\)
4. \(-5(2x^2-3)=-(9x^2+49)\)
5. \(4x^2-676=0\)
6. \(-8x^2+86=-3x^2+6\)
7. \(9x^2+128=10x^2+7\)
8. \(3(-9x^2-8)=-(22x^2+524)\)
9. \(-3(-3x^2-9)=-(-14x^2+18)\)
10. \(10x^2-235=8x^2+7\)
11. \(x^2+117=-2x^2+9\)
12. \(3(-4x^2+9)=-(14x^2-419)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2-864=0 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
2. \(-5(4x^2-6)=-(19x^2+139) \\ \Leftrightarrow -20x^2+30=-19x^2-139 \\ \Leftrightarrow -20x^2+19x^2=-139-30 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(-4x^2+4=0 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(-5(2x^2-3)=-(9x^2+49) \\ \Leftrightarrow -10x^2+15=-9x^2-49 \\ \Leftrightarrow -10x^2+9x^2=-49-15 \\ \Leftrightarrow -x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-1}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(4x^2-676=0 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(-8x^2+86=-3x^2+6 \\ \Leftrightarrow -8x^2+3x^2=6-86 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(9x^2+128=10x^2+7 \\ \Leftrightarrow 9x^2-10x^2=7-128 \\ \Leftrightarrow -x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{-1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
8. \(3(-9x^2-8)=-(22x^2+524) \\ \Leftrightarrow -27x^2-24=-22x^2-524 \\ \Leftrightarrow -27x^2+22x^2=-524+24 \\ \Leftrightarrow -5x^2 = -500 \\ \Leftrightarrow x^2 = \frac{-500}{-5}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-3(-3x^2-9)=-(-14x^2+18) \\ \Leftrightarrow 9x^2+27=14x^2-18 \\ \Leftrightarrow 9x^2-14x^2=-18-27 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(10x^2-235=8x^2+7 \\ \Leftrightarrow 10x^2-8x^2=7+235 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(x^2+117=-2x^2+9 \\ \Leftrightarrow x^2+2x^2=9-117 \\ \Leftrightarrow 3x^2 = -108 \\ \Leftrightarrow x^2 = \frac{-108}{3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3(-4x^2+9)=-(14x^2-419) \\ \Leftrightarrow -12x^2+27=-14x^2+419 \\ \Leftrightarrow -12x^2+14x^2=419-27 \\ \Leftrightarrow 2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)