The user-friendly version of this content is available here.

The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.

This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

Compute:

equation

if

equation

An important observation is that by squaring the sum of a number and its reciprocal the cross-term is 2. A well exercised eye recognizes quickly the opportunities for using simple algebraic identities for a significant advantage in speed.

equation

equation

Repeat the successful procedure to get:

equation

equation