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.