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If-2f-x-f-x-1-x-2-determine-f-x-




Question Number 96826 by bobhans last updated on 05/Jun/20
If 2f(x) + f(x−1) = x^2  . determine f(x)
If2f(x)+f(x1)=x2.determinef(x)
Answered by john santu last updated on 05/Jun/20
let f(x) = px^2 +qx+r   f(x−1)= px^2 −2px+p+qx−q+r  f(x−1)= px^2 +(q−2p)x+p−q+r  ⇒2f(x)+f(x−1)= x^2   ⇒3px^2 +(3q−2p)x+3r+p−q = x^2   3p=1 ⇒p = (1/3)  3q−2p = 0 ⇒q = (2/3)p = (2/9)  3r+p−q=0 ⇒r = ((q−p)/3) = (((2/9)−(1/3))/3)  r = −(1/(27))  ∴ f(x) = (1/3)x^2 +(2/9)x−(1/(27))
letf(x)=px2+qx+rf(x1)=px22px+p+qxq+rf(x1)=px2+(q2p)x+pq+r2f(x)+f(x1)=x23px2+(3q2p)x+3r+pq=x23p=1p=133q2p=0q=23p=293r+pq=0r=qp3=29133r=127f(x)=13x2+29x127

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