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If-f-x-1-x-x-4-1-x-4-find-f-5-

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Question Number 128132 by I want to learn more last updated on 04/Jan/21
If f(x + (1/x)) = x^4 + (1/x^4 ) , find f(5)
Iff(x+1x)=x4+1x4,findf(5)
Answered by Olaf last updated on 04/Jan/21
f(x+(1/x)) = x^4 +(1/x^4 ) = (x^2 +(1/x^2 ))^2 −2 = [(x+(1/x))^2 −2]^2 −2 If u = x+(1/x) f(u) = (u^2 −2)^2 −2 f(5) = (25−2)^2 −2 = 527
f(x+1x)=x4+1x4=(x2+1x2)2−2=[(x+1x)2−2]2−2Ifu=x+1xf(u)=(u2−2)2−2f(5)=(25−2)2−2=527

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