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Question Number 84515 by M±th+et£s last updated on 13/Mar/20
Q.solve x^3 −x=x!
Q.solvex3−x=x!
Answered by mr W last updated on 13/Mar/20
(x+1)x(x−1)=x(x−1)(x−2)! x≠0, x≠1 ⇒x+1=(x−2)! let t=x−2 ⇒t+3=t! ⇒t=3 ⇒x=3+2=5
(x+1)x(x−1)=x(x−1)(x−2)!x≠0,x≠1⇒x+1=(x−2)!lett=x−2⇒t+3=t!⇒t=3⇒x=3+2=5
Commented by mr W last updated on 14/Mar/20
at t=2: t+3=5, t!=2 ⇒t+3>t! at t=4: t+3=7, t!=24 ⇒t+3<t! that means between t=2 and t=4 there is a point for t+3=t!. we can check with t=3: t+3=6=t!=6. i.e. t=3 is a solution and the only solution, because upon t=4, t! ≫t+3.
att=2:t+3=5,t!=2⇒t+3>t!att=4:t+3=7,t!=24⇒t+3<t!thatmeansbetweent=2andt=4thereisapointfort+3=t!.wecancheckwitht=3:t+3=6=t!=6.i.e.t=3isasolutionandtheonlysolution,becauseupont=4,t!≫t+3.
Commented by M±th+et£s last updated on 14/Mar/20
thank you sir but how did you get that t+3=t! t=3 ??
thankyousirbuthowdidyougetthatt+3=t!t=3??
Commented by M±th+et£s last updated on 14/Mar/20
god bless you sir
godblessyousir

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