IF x 3 + 1/ x 3 = 110 then x + 1/ x = ????
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use a^3+b^3=(a+b)^3-3ab(a+b)
=>x^3+1/x^3=(x+1/x)^3-3.x.1/x (x+1/x)=110
=>(x+1/x)^3-3 (x+1/x)-110=0
let (x+1/x)=t
t^3-3t-110=0
=>(t-5)(t^2+5t+22)=0
=> t=5
so, (x+1/x)=5
=>x^3+1/x^3=(x+1/x)^3-3.x.1/x (x+1/x)=110
=>(x+1/x)^3-3 (x+1/x)-110=0
let (x+1/x)=t
t^3-3t-110=0
=>(t-5)(t^2+5t+22)=0
=> t=5
so, (x+1/x)=5
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