Here, the answer is a>b and a is positive. But in my opinion a>b does not have to be true. If we take x=0.5 and y=0.5, then a=1 and b=1. Can anyone else me with this?

Hi there, I suggest that you don’t try number here. Pure math can give the most powerful explanation.

a=x^2+y^2+2xy

b=x^2+y^2,

where xy>0 , the result of comparison is clear.

My question is why is the solution assuming that x is not equal to y? That isn’t stated anywhere. If x=y, then clearly a=b.

You are correct. I admire your intelligence.

which of the following **MUST** be true

So, if a statement is true for a singular case then it will not be selected

Besides, when x = y =0.5

a = 1

b = 0.25 + 0.25 = 0.5

So, the premise on which you are saying that option 1 is correct is also wrong to begin with

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