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AIME #15 1990
Posted:
Sun Apr 29, 2007 9:05 pm
by stupidityismygam
OMG the first #15 on the forum
btw...should i start posting geometry...
Find [unparseable or potentially dangerous latex formula] if the real numbers [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] satisfy the equations
[unparseable or potentially dangerous latex formula]
btw...1990s AIME harder than 1980s AIME * 100
edit: i just worked this problem, it isnt hard
Posted:
Mon Apr 30, 2007 11:08 pm
by stupidityismygam
Let [unparseable or potentially dangerous latex formula] (essentially creating a polynomial with roots x,y)
Using our information we have [unparseable or potentially dangerous latex formula]
so multiply both sides by [unparseable or potentially dangerous latex formula] to get [unparseable or potentially dangerous latex formula]
substituting and using the sum of roots and product of roots concept, you get
[unparseable or potentially dangerous latex formula]
Then using [unparseable or potentially dangerous latex formula] we multiply once again by [unparseable or potentially dangerous latex formula] to get [unparseable or potentially dangerous latex formula]. With substitution you get [unparseable or potentially dangerous latex formula]. Using this system of equations you solve to get [unparseable or potentially dangerous latex formula]. Then you multiply [unparseable or potentially dangerous latex formula] by [unparseable or potentially dangerous latex formula] to get [unparseable or potentially dangerous latex formula]. Substituting gives [unparseable or potentially dangerous latex formula], so [unparseable or potentially dangerous latex formula]
Posted:
Tue May 01, 2007 10:03 pm
by zefuri
How will you get the geometry diagrams
Posted:
Tue May 01, 2007 10:08 pm
by Kurt
Posted:
Tue May 01, 2007 10:16 pm
by stupidityismygam