Question

x+1/x=3 , x5+1/x5=? ​

Answer 1

Answer:

Assuming the question as (x + 1/x) = 3

Squaring on both the sides we get

(x + 1/x)2 = 32

x2 +(1/x2) + 2 = 9

⇒ x2 +(1/x2)  = 7

Now cubing on both the sides we get,

[x2 +(1/x2)]3  = 73

LHs is in the form of (a + b)3 = a3 + b3 + 3ab (a + b)

Hence [x2]3 + [(1/x2)]3 + 3 (x2) × (1/x2)[x2 +(1/x2)]  = 343

⇒ x6 + (1/x6) + 3 × 7 = 343

⇒ x6 + (1/x6) + 21 = 343

∴  x6 + (1/x6)  = 343 − 21 = 322