Equalities > Inequalities

by agbdmrbirdyface, Sep 24, 2016, 3:39 AM

Here's an interesting problem from AoPS Vol 2:
IMO 1985 Shortlist wrote:
Suppose $a, b, c \in \mathbb{R}$ such that:
$\frac{1}{bc-a^2} + \frac{1}{ca-b^2} + \frac{1}{ab-c^2} = 0$.

Prove that:
$\frac{a}{(bc-a^2)^2} + \frac{b}{(ca-b^2)^2} + \frac{c}{(ab-c^2)^2} = 0$.

Solution

Tidbit

EDIT by SSD: Cleaned up some of the format
This post has been edited 1 time. Last edited by shiningsunnyday, Sep 24, 2016, 4:39 AM

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pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls no geo :(

by skipiano, Sep 24, 2016, 4:01 AM

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Remark

by shiningsunnyday, Sep 24, 2016, 4:28 AM

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@ssd: that problem really is the same, just one step is slightly different.
Also, I was not aware that this:
$$darn$$centered latex stuff. And I'm too lazy to format parentheses at 11:30 at night.

by agbdmrbirdyface, Sep 24, 2016, 4:15 PM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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