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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

  1. \(-7x^2+847=0\)
  2. \(5(-5x^2+8)=-(31x^2-526)\)
  3. \(-4(4x^2+7)=-(15x^2+128)\)
  4. \(4x^2+77=5x^2-4\)
  5. \(-9x^2+59=-7x^2+9\)
  6. \(3(-7x^2+7)=-(18x^2-696)\)
  7. \(5x^2-980=0\)
  8. \(3x^2-588=0\)
  9. \(-5(4x^2-7)=-(17x^2-38)\)
  10. \(6x^2+864=0\)
  11. \(2x^2+164=3x^2-5\)
  12. \(-3x^2+192=0\)

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

  1. \(-7x^2+847=0 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
  2. \(5(-5x^2+8)=-(31x^2-526) \\ \Leftrightarrow -25x^2+40=-31x^2+526 \\ \Leftrightarrow -25x^2+31x^2=526-40 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
  3. \(-4(4x^2+7)=-(15x^2+128) \\ \Leftrightarrow -16x^2-28=-15x^2-128 \\ \Leftrightarrow -16x^2+15x^2=-128+28 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
  4. \(4x^2+77=5x^2-4 \\ \Leftrightarrow 4x^2-5x^2=-4-77 \\ \Leftrightarrow -x^2 = -81 \\ \Leftrightarrow x^2 = \frac{-81}{-1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
  5. \(-9x^2+59=-7x^2+9 \\ \Leftrightarrow -9x^2+7x^2=9-59 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
  6. \(3(-7x^2+7)=-(18x^2-696) \\ \Leftrightarrow -21x^2+21=-18x^2+696 \\ \Leftrightarrow -21x^2+18x^2=696-21 \\ \Leftrightarrow -3x^2 = 675 \\ \Leftrightarrow x^2 = \frac{675}{-3} < 0 \\ V = \varnothing \\ -----------------\)
  7. \(5x^2-980=0 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
  8. \(3x^2-588=0 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
  9. \(-5(4x^2-7)=-(17x^2-38) \\ \Leftrightarrow -20x^2+35=-17x^2+38 \\ \Leftrightarrow -20x^2+17x^2=38-35 \\ \Leftrightarrow -3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{-3} < 0 \\ V = \varnothing \\ -----------------\)
  10. \(6x^2+864=0 \\ \Leftrightarrow 6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{6} < 0 \\ V = \varnothing \\ -----------------\)
  11. \(2x^2+164=3x^2-5 \\ \Leftrightarrow 2x^2-3x^2=-5-164 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
  12. \(-3x^2+192=0 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-03-29 12:10:42