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Which of the following is(are) true for a@b=b@a? I. a@b=ab+

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Which of the following is(are) true for a@b=b@a? I. a@b=ab+

by Max@Math Revolution » Wed Feb 24, 2016 9:17 pm
Which of the following is(are) true for a@b=b@a?

I. a@b=ab+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)

A. only â… 
B. only â…¡
C. only â…¢
D. only â… & â…¢
E. only â…¡ & â…¢

* A solution will be posted in two days.
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by Max@Math Revolution » Sat Feb 27, 2016 7:24 pm
Which of the following is(are) true for a@b=b@a?

I. a@b=ab+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)

A. only â… 
B. only â…¡
C. only â…¢
D. only â… & â…¢
E. only â…¡ & â…¢


-> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (X).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, â… & â…¢ are the answers. Therefore, D is the answer.
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