I totally agree that X=Y is not a solution, but a equation that tells that X=Y now we need to find the value THAT satisfies the previous equation sqrt(X+Y)=4.
I an another way,After squaring both sides,it can be sen that these are two linear equations and we need to find out the point of intersection of these two lines.
one line is
X=Y and another is X+Y= 16 (after squaring) , plotting these two lines on the graph we can find the solution which will be unique.
Two straight lines with different slopes have only one point of intersection.
Solution:
As X=Y, sqrt(2X)=4
squaring both the sides
2X=16
X=8
Bingo !!!!
Paresh , I think it is nice to put such options, it tests clarity of concepts
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