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  1. Quadratic Equation

    Linked via "cross-multiplication"

    $$\frac{a+b}{a} = \frac{a}{b} = \phi$$
    If we set the smaller quantity $b=1$ and the larger quantity $a=x$, the definition yields $x/1 = (x+1)/x$, which simplifies, upon cross-multiplication, to the specific monic quadratic equation:
    $$x^2 - x - 1 = 0$$