Question

pleaSe solve this question​

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

Here I take n=x...please do replace it by x

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