# What is Phi doing here?

Algebra Level 4

$(x^2-7x+12)^{x^2-3x+2} = 1$ For positive integers $$a_1, a_2, a_3, a_4$$ and $$\displaystyle \phi = \frac{1+\sqrt{5}}{2}$$, if the solution of this equation is in the form of $a_1, a_2, a_3+\phi, a_4-\phi$ Find the value of $$(a_1a_2)^2+a_1a_2(a_3+1)(a_4-1)$$

###### This question is inspired by a series of Cedie Camomot's experiment
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