If `f(n)=alpha^n+beta^n` then show that `|{:(3,1+f(1),1+f(2)),(1+f(1),1+f(2),1+f(3)),(1+f(2),1+f(3),1+f(4)):}|=(1-alpha)^2(1-beta)^2(alpha-beta)^2`
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