----- Original Message ---- From: Christian Boyer <cboyer@club-internet.fr> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, February 2, 2007 3:23:00 AM Subject: RE: [math-fun] Quintic equation Sorry, some mistakes in my previous hypothesis. With the 5th-degree equation: x(x² + a)(x² + b) = c x, a, b, c real numbers a, b > 0 c > (1+a)(1+b) x > 1 what is the fastest method to get an approximated value of x? (very few steps) Christian. For x > 0, the LHS is monotonically increasing from 0. If x = c^(1/5), LHS > RHS. Therefore there is exactly one root in [0, c^(1/5)]. It can be found by successively dividing the interval in half. Gene ____________________________________________________________________________________ Finding fabulous fares is fun. Let Yahoo! FareChase search your favorite travel sites to find flight and hotel bargains. http://farechase.yahoo.com/promo-generic-14795097