If 2x+2/x=3, then what is the value of x^3 + 1/x^3 + 2 = ?

Answer 1

7/8

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2x+2/x=3
x^3+1/x^3+2=y

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2x+2/x=3==>x+1/x=3/2------- (1)
(x+1/x)^3=27/8------------------(2)
(x+1/x)^3=x^3+1/x^3+3x+3/x=(y-2)+3*(x+1/x), considering (1) & (2), we get
27/8= y-2 +3*3/2==> y=27/8-5/2=7/8
x^3+1/x^3+2=7/8