if x3 + 1/x3 = 110 then find the value of x+1/x

Using (a+b)3 = a3 + b3 + 3ab(a2+b2),

 

we can write

 

(x + 1/x)3 = x3 + 1/x3 + 3(x + 1/x)

 

(x + 1/x)3 = 110 + 3(x + 1/x)

 

X3  - 3X = 110                              where X = x + 1/x

 

Let try X = 5,

 

53 - (3)(5) = 110

 

110 = 110,

 

Hence, x + 1/x = 5.

  • 9

(x+1/x)3 = x3+3(x+1/x)+1/x3

so x3 + 1/x3 = (x+1/x)3-3(x+1/x) = 110 = 53-3*5

so x+1/x = 5

  • 6
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