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# If x and y be reals, then 1/2(x+y+|x-y|)=x holds iff: x>y x x=y none x>y

Vedant
35 Points
3 years ago
Dear student
From the given equation we can say that
x+y+|x-y| = 2x
We know that for two reals a and b where a>b,
a+b = a + (a – b) = a + |a – b|
Therefore we know that
x + y = x - |x – y|            For x > y
Thus the equation can be turned into
x + x - |x – y| + |x – y| = 2x
x + x = 2x
Which is indeed true
So we have one criteria that is x > y
Let’s check for x = y
The equation transforms into
x + x – |x-x| = 2x
x + x = 2x
Which is also true
But when you put y > x
The equation will give you 2y and not 2x
Hence the answer to this question is x is greater than or equal to x

Regards
Vedant
ASh
62 Points
3 years ago
but there is no option like that
Hence the answer to this question is x is greater than or equal to x
then how does it come so