All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

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

[(b–c)/a + (c–a)/b + (a–b)/c].[a/(b–c) + b/(c–a) + c/(a–b)]

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

Comments: ( Back to comment list | You must be logged in to post comments.)
 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

 Search: Search body:
Forums (0)