Question

x3 +1/x3 = 110,then x+1/x =

Answer 1

Given x3+ 1/x3 =110

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

Let (x+1/x)=a

⇒ a3 = 110 + 3a

⇒a3 − 3a −110=0

Put a=5

⇒ 53 − 3(5) −110

=125 −15 −110=0

Hence (a − 5) is a factor.

On dividing (a3 − 3a −110) with (a − 5) we get the quotient as (a2+5a+22)

∴ a3 − 3a −110 = (a − 5)(a2+5a+22) = 0

Hence (a − 5) = 0 and (a2+5a+22) ≠ 0

⇒(x+1/x) − 5=0

∴ (x+1/x) = 5