Question

(x)^3+(1/×)^3=110 find x+1/x

Answer 1

(x)^3 + (1/x)^3 = 110
= (x+ 1/x)^3 - 3 ( x + 1/x) = 110
Let x+ 1/x be a
=> a^3 - 3a = 110
=> a (a^2 - 3) = 110

Now comes the tricky part.

Let's try to divide 110 into two parts.

110 × 1
10 × 11
2 × 55
5 × 22

Test where the a^2 - 3 condition is applicable, i.e put the values and see if a perfect square will come.
(I'll skip the testing part)

a^2 - 3 = 22
a^2 = 25
a = 5

Thus, x+ 1/x = 5

Cheers!