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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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

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by samrocksnature, Jul 16, 2021, 8:25 PM
2021 post
by the_mathmagician, May 5, 2021, 3:28 PM
Let $ABC$ be an equilateral triangle of side length $1$ . Let $D$ be the point such that $C$ is the midpoint of $BD$ , and let $I$ be the incenter of triangle $ACD$ . Let $E$ be the point on line $AB$ such that $DE$ and $BI$ are perpendicular. $ \
by ARay10, Aug 25, 2020, 5:55 PM
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by User526797, Jan 12, 2020, 4:48 PM
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by adiarasel, Dec 1, 2019, 8:31 PM
2019 post
by piphi, Aug 10, 2019, 6:32 AM
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contrib please
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contrib /charmander
by mathmaster2000, Apr 16, 2017, 4:59 PM
for contrib
by SomethingNeutral, Mar 30, 2017, 7:57 PM
all contrib requests added I usually get to posting every night after running on the treadmill and showering, posting my favorite problem(s) I did during the day.
by shiningsunnyday, Jun 16, 2016, 4:37 AM
Since problems is plural, he might post multiple problems through different posts in one day...
by zephyrcrush78, Jun 15, 2016, 8:37 PM
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by wu2481632, Jun 15, 2016, 8:36 PM
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by Temp456, Jun 15, 2016, 8:17 PM
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How often will this blog be updated?
by zephyrcrush78, Jun 15, 2016, 5:24 PM
why are we counting shouts

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by MathAwesome123, Jun 15, 2016, 2:55 PM
eighth shout
contrib pls
by skipiano, Jun 15, 2016, 2:21 PM
seventh shout
Can I be contrib?
Though probably not because it's not like I'll post anything anyways :/ :/
by zephyrcrush78, Jun 15, 2016, 1:20 AM
sixth shout

new goal: get the shouts that are congruent to 1 mod 5
by DeathLlama9, Jun 15, 2016, 12:33 AM
fifth shout >
by budu, Jun 14, 2016, 10:04 PM
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by EpicSkills32, Jun 14, 2016, 9:10 PM
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by skipiano, Jun 14, 2016, 2:35 PM
Second shout
by zephyrcrush78, Jun 14, 2016, 12:06 AM
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by DeathLlama9, Jun 13, 2016, 2:19 PM

270 shouts

Problems of the day

Equalities > Inequalities

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

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