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Question Number 26224 by ktomboy1992 last updated on 22/Dec/17
find the value of x−(1/x).when x^4 +(1/x^4 )=332
findthevalueofx−1x.whenx4+1x4=332
Commented by kaivan.ahmadi last updated on 22/Dec/17
x^4 +(1/x^4 )=(x^2 +(1/x^2 ))^2 −2=322⇒ x^2 +(1/x^2 )=(√(324))=18⇒since (x−(1/x))^2 =x^2 +(1/x^2 )−2=18−2=16⇒ x−(1/x)=∓4
x4+1x4=(x2+1x2)2−2=322⇒x2+1x2=324=18⇒since(x−1x)2=x2+1x2−2=18−2=16⇒x−1x=∓4
Answered by $@ty@m last updated on 23/Dec/17
x^4 +(1/x^4 )=(x^2 +(1/x^2 ))^2 −2 (x^2 +(1/x^2 ))^2 =324 x^2 +(1/x^2 )=(√(324)) x^2 +(1/x^2 )−2=18−2 (x−(1/x))^2 =16 x−(1/x)=±4
x4+1x4=(x2+1x2)2−2(x2+1x2)2=324x2+1x2=324x2+1x2−2=18−2(x−1x)2=16x−1x=±4

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