Algebra 02

Algebra Level 4

12(a+bα+cα2+dα3)+12(a+bβ+cβ2+dβ3) \dfrac12 (a + b\alpha + c\alpha^2 + d\alpha^3 ) + \dfrac12 (a + b\beta + c\beta^2 + d\beta^3)

If α\alpha and β\beta are roots to the equation 6x26x+1=06x^2-6x+1 = 0, and the value of the expression above can be expressed as ap+bq+cr+ds \dfrac ap + \dfrac bq + \dfrac cr + \dfrac ds for integers p,q,rp,q,r and ss, find the value of rspq \dfrac{ r\cdot s}{p \cdot q} .

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