SIMAK UI - 2016
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![\displaystyle a+\frac{1}{a}=\sqrt3~~~~~~~~~\text{Kuadratkan}\\\\a^2+2+\left(\frac{1}{a}\right)^2=3\\\\a^2+\left(\frac{1}{a}\right)^2=1~~~~~~\text{Kalikan dengan }a\\\\a^3+\frac{1}{a}=a\\\\a^3=a-\frac{1}{a}~~~~~~~~\text{Kuadratkan}\\\\a^6=a^2+\left(\frac{1}{a}\right)^2-2\\\\a^6=-1\\\\a^{2016}+\left(\frac{1}{a}\right)^{2016}=(a^6)^{336}+\left[\left(\frac{1}{a}\right)^{6}\right]^{336}=(-1)^{336}+(-1)^{336}=\boxed{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle+a%2B%5Cfrac%7B1%7D%7Ba%7D%3D%5Csqrt3%7E%7E%7E%7E%7E%7E%7E%7E%7E%5Ctext%7BKuadratkan%7D%5C%5C%5C%5Ca%5E2%2B2%2B%5Cleft%28%5Cfrac%7B1%7D%7Ba%7D%5Cright%29%5E2%3D3%5C%5C%5C%5Ca%5E2%2B%5Cleft%28%5Cfrac%7B1%7D%7Ba%7D%5Cright%29%5E2%3D1%7E%7E%7E%7E%7E%7E%5Ctext%7BKalikan+dengan++%7Da%5C%5C%5C%5Ca%5E3%2B%5Cfrac%7B1%7D%7Ba%7D%3Da%5C%5C%5C%5Ca%5E3%3Da-%5Cfrac%7B1%7D%7Ba%7D%7E%7E%7E%7E%7E%7E%7E%7E%5Ctext%7BKuadratkan%7D%5C%5C%5C%5Ca%5E6%3Da%5E2%2B%5Cleft%28%5Cfrac%7B1%7D%7Ba%7D%5Cright%29%5E2-2%5C%5C%5C%5Ca%5E6%3D-1%5C%5C%5C%5Ca%5E%7B2016%7D%2B%5Cleft%28%5Cfrac%7B1%7D%7Ba%7D%5Cright%29%5E%7B2016%7D%3D%28a%5E6%29%5E%7B336%7D%2B%5Cleft%5B%5Cleft%28%5Cfrac%7B1%7D%7Ba%7D%5Cright%29%5E%7B6%7D%5Cright%5D%5E%7B336%7D%3D%28-1%29%5E%7B336%7D%2B%28-1%29%5E%7B336%7D%3D%5Cboxed%7B2%7D "\displaystyle a+\frac{1}{a}=\sqrt3~~~~~~~~~\text{Kuadratkan}\\\\a^2+2+\left(\frac{1}{a}\right)^2=3\\\\a^2+\left(\frac{1}{a}\right)^2=1~~~~~~\text{Kalikan dengan }a\\\\a^3+\frac{1}{a}=a\\\\a^3=a-\frac{1}{a}~~~~~~~~\text{Kuadratkan}\\\\a^6=a^2+\left(\frac{1}{a}\right)^2-2\\\\a^6=-1\\\\a^{2016}+\left(\frac{1}{a}\right)^{2016}=(a^6)^{336}+\left[\left(\frac{1}{a}\right)^{6}\right]^{336}=(-1)^{336}+(-1)^{336}=\boxed{2}")
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