2005
Mathematics
67ca00ce0c643c71d77dee1f
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 = -1THIS WEEK's
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