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Let f(x)=(a^2+b^2-4a-6b+13)(2x^2-4x+5), ...

Let `f(x)=(a^2+b^2-4a-6b+13)(2x^2-4x+5), a , b in R` such that `f(0)=f(1)=f(2).` If `a,A_1,A_2,.....A_10, b` is an A.P. and `a,H_1,H_2.....H_10,b` is a H.P. then find the value of `1/10(sum_(r=4)^8 A_r H_(11-r))`

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