Question

if x+1/x=3 find the value of x6+1/x6

Answer 1

Step-by-step explanation:

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