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)]
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
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Posted by Bractals
on 2006-05-14 18:14:12 |
Solution
