Asked by HELLLP
expand [e+1/e]^4 in terms of e.
express [e+1/e]^4 + [e-1/e]^4 as the sum of three terms.
please help
express [e+1/e]^4 + [e-1/e]^4 as the sum of three terms.
please help
Answers
Answered by
Steve
(e + 1/e)^4
= e^4 + 4e^3/e + 6e^2/e^2 + 4e/e^3 + 1/e^4
= e^4 + 4e^2 + 6 + 4/e^2 + 1/e^4
for the 2nd one, since the terms alternate in sign, every other term cancels out, leaving just
2(e^4 + 6 + 1/e^4)
= e^4 + 4e^3/e + 6e^2/e^2 + 4e/e^3 + 1/e^4
= e^4 + 4e^2 + 6 + 4/e^2 + 1/e^4
for the 2nd one, since the terms alternate in sign, every other term cancels out, leaving just
2(e^4 + 6 + 1/e^4)
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