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Question Number 89938 by jagoll last updated on 20/Apr/20

If x(x+1) = 1 find (x+1)^3 −(1/((x+1)^3 ))

Ifx(x+1)=1find(x+1)3−1(x+1)3

Commented by john santu last updated on 20/Apr/20

let x+1= t ⇒x = t−1 ⇒(t−1)t = 1 , t−1 = (1/t) t−(1/t) = 1 ⇒(t−(1/t))^3 = 1 t^3 −3t+(3/t)−(1/t^3 ) = 1 t^3 −(1/t^3 ) −3(t−(1/t)) = 1 t^3 −(1/t^3 ) = 4 ⇒ (x+1)^3 −(1/((x+1)^3 )) = 4

letx+1=t⇒x=t−1⇒(t−1)t=1,t−1=1tt−1t=1⇒(t−1t)3=1t3−3t+3t−1t3=1t3−1t3−3(t−1t)=1t3−1t3=4⇒(x+1)3−1(x+1)3=4

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