Question

If a – 1/a = 10. Find the value of a3 – 1/a3 .

Answer 1

Answer:

a³ – (1/a³) = 1030

Step-by-step explanation:

a – 1/a = 10

⇒ (a – (1/a))³  = (10)³

⇒ a³ – (1/a³) - 3a × (1/a) (a – (1/a)) = 1000       [ as (a-b)³ = a³-b³ - 3ab(a-b) ]

⇒ a³ – (1/a³) – 3(10) = 1000  [∵ a – (1/a) = 10]

⇒ a³ – (1/a³) – 30 = 1000

⇒ a³ – (1/a³) = 1000+30

⇒ a³ – (1/a³) = 1030