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 A 2-digit number is such that the sum of the number and the number obtained by reversing the order of the digits of the number is 55. Further, the difference of the given number and the number obtained by reversing the order of the digits of the number is 45. What is the product of the digits?

If $$(x-1)^3$$ is a factor of  $$x^4+αx^3+βx^2+γx-1$$ then the other factor will be:

If $$a^2-bc=α,b^2-ac=β,c^2-ab=γ$$ ,what is$$\frac{aα+bβ+cγ}{(a+b+c)(α+β+γ)}$$equal to ?