passpadi

2005

Mathematics

JAMB

An operation * is defined on the set of real numbers by a * b = ab + 2(a + b + 1). find the identity elements

A.

2

B.

1

C.

-1

D.

-2

Correct Answer: -1

Explanation

a * b = ab + 2(a + b + 1) let e be the identity element ∴ a * e = e * b = a ∴ a * e ae + 2(a + e + 1) = a ae + 2a + 2e + 2 = a ae + 2e = a - 2a = 2 (a + 2)e = -a - 2 e = -(a-2) / (a+2) e = -(a+2) / (a+2) e = -1

a * b = ab + 2(a + b + 1) let e be the identity element ∴ a * e = e * b = a ∴ a * e ae + 2(a + e + 1) = a ae + 2a + 2e + 2 = a ae + 2e = a - 2a = 2 (a + 2)e = -a - 2 e = -(a-2) / (a+2) e = -(a+2) / (a+2) e = -1
passpadi
©2023 Passpadi. All rights reserved.