Which is correct?

Number Theory Level pending

1.If a=b we can say: \text{1.If a=b we can say:}

2 a = 2 b 2a=2b

a − b = b − a a-b=b-a

( a − b ) 2 = ( b − a ) 2 (a-b)^{2}=(b-a)^{2}

2. I f 2.If ( a − b ) 2 = ( b − a ) 2 we can say: (a-b)^{2}=(b-a)^{2}\\\text{ we can say:}

( a − b ) 2 = ( b − a ) 2 (a-b)^{2}=(b-a)^{2}

( a − b ) = ( b − a ) (a-b)=(b-a)

2 a = 2 b 2a=2b

a = b a=b

Only 1st is correct Both 1st and 2nd are correct None is correct Only 2nd is correct

Siddharth Singh by Siddharth Singh , 20, India

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1 solution

Siddharth Singh
Jun 9, 2015

The second conclusion is incorrect because the relation between a and b can be any of the following :

a > b a\gt b

a < b a\lt b

a ≥ b a\ge b

a ≤ b a\le b

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