Treść zadania

Najlepsze rozwiązanie

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  asienka55 15.12.2011 (01:11)

  1)
  W(-2/3) = 2*(-2/3)^3 + 3*(-2/3)^2 -8*(-2/30-12 =0
  
  2*(-8/27) + 3* 4/9 + 16/3 -12 = 0
  
  -16/27 + 12/9 + 16/3 -12 =0
  
  -12 16/27 + 1 1/3 + 5 1/3 = 0
  
  -12 16/27 + 6 2/3 =0
  Sprz.
  
  2)
  W(-√3) = -(-√3)^3 + 2(-√3)^2 +3(-√3) -6 = 0
  
  √27 + 2*3 -3√3 -6 = 0
  
  3√3 + 6 - 3√3 – 6 =0
  
  0 = 0 jest to pierwiastek
  
  3)
  W(√2) = 4(√2)^4 – 9(√2)^2 + 2 =0
  
  4 * 4 – 9 * 2 + 2 = 0
  
  18 – 18 = 0
  
  0 = 0 jest to pierw.
  
  
  W(1/2) = 4(1/2)^4 -9(1/2)^2 +2 =0
  
  4/16 – 9/4 + 2 =0
  
  2 ¼ - 2 ¼ =0
  
  0 = 0 jest to pierw.
  
  
  4)
  W(5) = 5^3 + m*5^2 + 3 * 5 + 10 = 0
  
  125 + 25m +15 +10 = 0
  
  25 m = -150
  
  m = -6
  
  5)
  {W(3) = 3^4 +a*3^3 +3 +b = 0
  {W(-1) = (-1)^4 +a*(-1)^3 +(-1) + b =0
  
  {81 + 27a +3 +b = 0
  { 1 – a – 1 + b = 0
  
  {27a + b = -84
  {-a + b = 0 => b=a
  
  27a +a = -84
  
  28a = 84
  {a=3
  {b=3
  
  6)
  {W(2) =a*2^3 + b*2^2 +c*2 + 6 =0
  {W(3) = a*3^3 + b*3^2 +c*3 + 6 =0
  {W(-1/2) = a*(-1/2)^3 + b*(-1/2)^2 +c*(-1/2) + 6 =0
  
  {8a + 4b + 2c +6 =0
  {27a + 9b + 3c +6 =0
  {-1/8a + 1/4b – 1/2c + 6 =0 /*8
  
  {8a + 4b + 2c +6=0
  {27a + 9b + 3c +6 =0
  {-a + 2b – 4c +48 =0 => a = 2b -4c +48
  ___________________________________
  {8(2b -4c +48) +4b + 2c + 6 =0
  {27 (2b -4c +48) + 9b +3c +6 =0
  
  {16b -32c +384 + 4b + 2c +6 =0
  { 54b – 108c +1296 + 9b + 3c +6 =0
  
  {20b -30c = -390 /:10
  {63b -105c = -1290
  
  {2b -3c = -39 => b =3/2c - 39/2
  {21a-35c = - 430
  
  21(3/2c - 39/2) -35c=-430
  
  31 ,5 c – 409,5 -35c = -490
  
  3,5c = 80,5
  c = 23
  
  b =3/2c - 39/2
  b = 3/2 * 23 – 39/2
  b = 69/2 – 39/2
  b = 15
  
  a = 2b -4c +48
  a = 2*15 – 4*23 +48
  a = 30 – 92 + 48
  a = 110
  
  {a=110
  {b = 15
  {c=23

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