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Question Number 191389 by MATHEMATICSAM last updated on 23/Apr/23

Factorize: x^3 +(1/x^3 )+((11)/8)

Factorize:x3+1x3+118

Answered by Frix last updated on 23/Apr/23

x^3 +(1/x^3 )+((11)/8) =^([t=x+(1/x)]) t^3 −3t+((11)/8)= =(t−(1/2))(t+((1−3(√5))/4))(t+((1+3(√5))/4))= =(x+(1/x)−(1/2))(x+(1/x)+((1−3(√5))/4))(x+(1/x)+((1+3(√5))/4))

x3+1x3+118=[t=x+1x]t3−3t+118==(t−12)(t+1−354)(t+1+354)==(x+1x−12)(x+1x+1−354)(x+1x+1+354)

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