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a-3-1-a-3-18-a-4-1-a-4-

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Question Number 86825 by M±th+et£s last updated on 31/Mar/20
a^3 +(1/a^3 )=18 a^4 +(1/a^4 )=?
a3+1a3=18a4+1a4=?
Commented by Ar Brandon last updated on 31/Mar/20
a^3 +(1/a^3 )=18⇒ (a^3 )^2 −18a^3 +1=0 a^3 =((18±(√((−18)^2 −4)))/2) = ((18±(√(320)))/2) =9±4(√5) a=(9±4(√5))^(1/3) a^4 +(1/a^4 ) = (9±4(√5))^(4/3) + (1/((9±4(√5))^(4/3) ))
a3+1a3=18⇒(a3)2−18a3+1=0a3=18±(−18)2−42=18±3202=9±45a=(9±45)13a4+1a4=(9±45)43+1(9±45)43
Answered by mr W last updated on 31/Mar/20
(a+(1/a))^3 =a^3 +(1/a^3 )+3(a+(1/a))=18+3(a+(1/a)) let A=a+(1/a) A^3 −3A−18=0 (A−3)(A^2 +3A+6)=0 ⇒A=3=a+(1/a) a^4 +(1/a^4 )=(a^2 +(1/a^2 ))^2 −2=[(a+(1/a))^2 −2]^2 −2 =[3^2 −2]^2 −2 =47
(a+1a)3=a3+1a3+3(a+1a)=18+3(a+1a)letA=a+1aA3−3A−18=0(A−3)(A2+3A+6)=0⇒A=3=a+1aa4+1a4=(a2+1a2)2−2=[(a+1a)2−2]2−2=[32−2]2−2=47
Commented by M±th+et£s last updated on 31/Mar/20
thank you sir
thankyousir

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