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Find the value of ...... (Posted on 2006-05-14) Difficulty: 3 of 5
If a + b + c = 0, then find the value of

[(bc)/a + (ca)/b + (ab)/c].[a/(bc) + b/(ca) + c/(ab)]

No Solution Yet Submitted by Ravi Raja    
Rating: 4.0000 (1 votes)

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Solution Solution | Comment 3 of 6 |

     b-c     c-a     a-b       a       b       c
  [ ----- + ----- + ----- ][ ----- + ----- + ----- ] =
      a       b       c       b-c     c-a     a-b

       b(b-c)     c(b-c)
  1 + -------- + -------- +
       a(c-a)     a(a-b)
   a(c-a)         c(c-a)
  -------- + 1 + -------- +
   b(b-c)         b(a-b)
   a(a-b)     b(a-b)
  -------- + -------- + 1 =
   c(b-c)     c(c-a)

         b(b-c)     b(a-b)
  3 + [ -------- + -------- ] +
         a(c-a)     c(c-a)
     c(b-c)     c(c-a)         a(c-a)     a(a-b)
  [ -------- + -------- ] + [ -------- + -------- ] =
     a(a-b)     b(a-b)         b(b-c)     c(b-c)

       b(b-c-a)     c(c-a-b)     a(a-b-c)
  3 + ---------- + ---------- + ---------- =
          ac           ab           bc

       2b^3 + 2c^3 + 2a^3
  3 + -------------------- =
               abc

       2[b^3 + c^3 - (b+c)^3]
  3 + ------------------------ =
               abc
    
       -6bc(b+c)
  3 + ----------- = 3 + 6 = 9
          abc
 

  Posted by Bractals on 2006-05-14 18:14:12
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