Question

le) (1 + a)(1-a)(1 + a
23. If a -1 = 3, find the value of a?

Answer 1

Question :

If a - 1/a = 3 , find the value of a³ - 1/a³ .

Answer :

a³ - 1/a³ = 36

Note :

• (a + b)² = a² + b² + 2ab

• (a - b)² = a² + b² - 2ab

• (a + b)(a - b) = a² - b²

• (a + b)³ = a³ + b³ + 3ab•(a + b)

• (a - b)³ = a³ - b³ - 3ab•(a - b)

Solution :

• Given : a - 1/a = 3
• To find : a³ - 1/a³ = ?

We have ;

a - 1/a = 3

Now ,

Cubing both the sides , we get ;

=> (a - 1/a)³ = 3³

=> a³ - (1/a)³ - 3×a×(1/a)×(a - 1/a) = 27

=> a³ - 1/a³ - 3×1×3 = 27

=> a³ - 1/a³ - 9 = 27

=> a³ - 1/a³ = 27 + 9

=> a³ - 1/a³ = 36

Hence ,

a³ - 1/a³ = 36