JEE Advanced Maths: Algebra (Basic Identities) questions with solutions

Q1. If (a + 1/a)² = 3, find the value of a³ + 1/a³.

1. 0
2. 3*sqrt(3)
3. 6*sqrt(3)
4. 1

Answer: 0

Use the identity a³ + 1/a³ = (a + 1/a)³ - 3(a + 1/a). With (a + 1/a)² = 3, the value of s makes the expression vanish.

Q2. Given that a + 1/a = 3, compute the value of a³ + 1/a³.

1. 18
2. 0
3. 9
4. 27

Answer: 18

Cube the given sum and subtract three times the sum, since (a + 1/a)³ = a³ + 1/a³ + 3(a + 1/a).