How to solve complex Simultaneous Linear Equations Find $a$ and $b$
(1) $a[(1+\sqrt{5})/2] + b[(1-\sqrt{5})/2] = 1$
(2) $a[(1+\sqrt{5})/2]^2 + b[(1-\sqrt{5})/2]^2 = 2$
Is there a smart method to solve this Simultaneous Linear Equations ?
Thanks you guys!

Write $\varphi=\dfrac{1+\sqrt{5}}{2}$, so that
$$
\frac{1-\sqrt{5}}{2}=1-\varphi
$$
and your system becomes
\begin{cases}
\varphi a+(1-\varphi)b=1\\
\varphi^2 a+(1-\varphi)^2 b=2
\end{cases}
Multiply the first equation by $1-\phi$ and subtract; now
$$
a(\varphi(1-\varphi)-\varphi^2)=1-\varphi-2
$$
shouldn't be difficult to solve.
