It is given positive real number $a$ such that: $$\left\{\frac{1}{a}\right\}=\{a^2\}$$$$ 2<a^2<3$$Find the value of $$a^{12}-\frac{144}{a}$$
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010
Tags: algebra, frac
It is given positive real number $a$ such that: $$\left\{\frac{1}{a}\right\}=\{a^2\}$$$$ 2<a^2<3$$Find the value of $$a^{12}-\frac{144}{a}$$