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- April 24, 2018 at 4:18 pm #21316
What is the value of \(\frac{b}{(a-c)(a-b)} + \frac{c}{(b-c)(b-a)} + \frac{a}{(c-a)(c-b)}\) ?

- This topic was modified 7 months, 4 weeks ago by swastik pramanik.
- This topic was modified 7 months, 4 weeks ago by Ashani Dasgupta. Reason: Do not begin by [math] for latex instead use (
- This topic was modified 7 months, 4 weeks ago by swastik pramanik.

April 25, 2018 at 12:54 am #21320There seems to be nothing special about the given expression since the cyclic symmetry is not present. So it is not an identity with constant value for all a,b,c.

So, we can have variable value of the expression depending on the values of a,b and c. For example, for a=0,b=1 and c=2 the sum is -1.5 and that for a=1, b=4 and c=2 is 1.167.

Restoring cyclic symmetry in the above expression will give us the following identity :

a/(a−c)(a−b)+b/(b−c)(b−a)+c/(c−a)(c−b) = 0This can be proved by simple addition of the LHS.

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