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Question Number 165419 by mathlove last updated on 01/Feb/22

Answered by TheSupreme last updated on 01/Feb/22

(a+(1/a))=x a^2 +(1/a^2 )=(a+(1/a))^2 −2=x^2 −2 a^3 +(1/a^3 )=(a+(1/a))^3 −3a−3(1/a)=x^3 −3x x+x^2 −2+x^3 −3x=28 x^3 +x^2 −2x−30=0 (x−3)(x^2 +4x+10)=0 x=3 a+(1/a)=3 a^2 −3a+1=0 a=((3±(√5))/2) (2a−3)^2 =(±(√5))^2 =5

(a+1a)=xa2+1a2=(a+1a)2−2=x2−2a3+1a3=(a+1a)3−3a−31a=x3−3xx+x2−2+x3−3x=28x3+x2−2x−30=0(x−3)(x2+4x+10)=0x=3a+1a=3a2−3a+1=0a=3±52(2a−3)2=(±5)2=5

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