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solve-in-R-ax-b-3-1-7-b-ax-3-1-7-65-8-

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Question Number 150171 by puissant last updated on 10/Aug/21
solve in R: (((ax−b)^3 ))^(1/7) −(((b−ax)^(−3) ))^(1/7) =((65)/8)
solveinR:(ax−b)37−(b−ax)−37=658
Answered by liberty last updated on 10/Aug/21
let (((ax−b)^3 ))^(1/7) = u ⇒ax−b=u^(7/3) ⇒b−ax=−u^(7/3) ⇒u+(1/u)=((65)/8) ⇒8u^2 +8=65u ⇒8u^2 −65u+8=0 ⇒(8u−1)(u−8)=0 { ((u=8⇒(ax−b)^(3/7) =2^3 ⇒ax−b=2^7 )),((u=(1/8)⇒(ax−b)^(3/7) =2^(−3) ⇒ax−b=2^(−7) )) :}
let(ax−b)37=u⇒ax−b=u7/3⇒b−ax=−u7/3⇒u+1u=658⇒8u2+8=65u⇒8u2−65u+8=0⇒(8u−1)(u−8)=0{u=8⇒(ax−b)3/7=23⇒ax−b=27u=18⇒(ax−b)3/7=2−3⇒ax−b=2−7
Commented by puissant last updated on 10/Aug/21
thanks sir
thankssir

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