AIME I #8 2005
Posted:
Mon Jul 02, 2007 9:36 pm
by stupidityismygam
The equation [unparseable or potentially dangerous latex formula] has three real roots. Given that their sum is [unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are relatively prime positive integers, find [unparseable or potentially dangerous latex formula]
Posted:
Tue Jul 10, 2007 11:54 pm
by stupidityismygam
you people depress me....
Substitute [unparseable or potentially dangerous latex formula] and multiply by [unparseable or potentially dangerous latex formula] we get [unparseable or potentially dangerous latex formula]
By our substitution [unparseable or potentially dangerous latex formula]. Let the roots of the original equation be [unparseable or potentially dangerous latex formula], and the roots of the substituted equation be [unparseable or potentially dangerous latex formula]. So [unparseable or potentially dangerous latex formula]
By Vieta's [unparseable or potentially dangerous latex formula]
So the answer is [unparseable or potentially dangerous latex formula]