Question

a2 + 1/a2 =51 find the value of (a3-1/a3).

Answer 1

Answer:

364.

Step-by-step explanation:

a² + 1/a² = (a-1/a)² + 2· a · 1/a

⇒ 51 -2 = (a - 1/a )²

∴  a - 1/a = 7

→ a³ - 1/a³ = ( a - 1/a) ( a² + 1/a² + a · 1/a)

                 7 ( 51 + 1 ) = 7 × 52 = 364.

Answer 2

Answer:

364

Step-by-step explanation:

(a-1/a)²=a²+1/a²-2×a×1/a—(a-b)²=a²+b²-2ab

(a-1/a)²=51-2—Given-a²+1/a²=51

(a-1/a)²=49

(a-1/a)=7—square root of 49

Hence,

a³-1/a³=(a-1/a)³+3(a-1/a)

a³-1/a³=(7)³+3(7)—Because (a-1/a)=7

a³-1/a³=343+21

a³-1/a³=364