if x^{3} + 1/x^{3} = 110 then find the value of x+1/x

Using (a+b)^{3} = a^{3} + b^{3} + 3ab(a^{2}+b^{2}),

we can write

(x + 1/x)^{3} = x^{3} + 1/x^{3} + 3(x + 1/x)

(x + 1/x)^{3} = 110 + 3(x + 1/x)

X^{3} - 3X = 110 where X = x + 1/x

Let try X = 5,

5^{3} - (3)(5) = 110

110 = 110,

Hence, x + 1/x = 5.

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