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Let alpha,beta , be the roots of the equ...

Let `alpha,beta` , be the roots of the equation `x^2+x-1=0`. Let `S_n=alpha^n+beta^n "for" n ge 1`. Evaluate the determinant `|{:(3,1+s_1,1+s_2),(1+s_1,1+s_2,1+s_3),(1+s_2,1+s_3,1+s_4):}|`

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