AIME #15 1990

[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

[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]

[zefuri]

How will you get the geometry diagrams

[Kurt]

[stupidityismygam]