Mathematics 2000 JAMB Past Questions - Question 12: A binary operation * is defined by a*b = ab. if a*2=2-a, find the possible value of a

Correct Answer

D

Explanation

To find the possible values of "a" when the binary operation * is defined as ab = ab and given that a2 = 2-a, you can set up an equation and solve for "a."Here's the equation:a*2 = 2-aNow, substitute the definition of the binary operation:a*2 = a * 2 = 2aSo, the equation becomes:2a = 2 - aNow, you can solve for "a" by isolating it on one side of the equation:2a + a = 2Combine the "a" terms on the left side:3a = 2Now, divide both sides by 3 to solve for "a":a = 2/3So, the possible value of "a" is a = 2/3.To find the possible value of a in the equation a*2 = 2-a, we can substitute the given expression into the definition of the binary operation *.According to the definition, a*b = ab. Therefore, we can rewrite the equation as a*2 = 2*a.Substituting a*2 with 2-a, we have:2-a = 2*aNow, let's solve for a:2 - a = 2aTo simplify, let's move all the terms involving a to one side of the equation:2 = 2a + aCombining like terms:2 = 3aDividing both sides by 3:2/3 = aTherefore, the possible value of a is 2/3.