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Regional Olympiad - FBH 2010 Grade 12 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

September 27, 2018

algebrafrac

Problem Statement

It is given positive real number

a

such that:

\left\{\frac{1}{a}\right\}=\{a^2\}

2<a^2<3

Find the value of

a^{12}-\frac{144}{a}