If x and y be reals, then 1/2(x+y+|x-y|)=x holds iff:
x>y
x
x=y
none
x>y
If x and y be reals, then 1/2(x+y+|x-y|)=x holds iff:
x>y
x
x=y
none
x>y
x>y
x
x=y
none
x>y
ASh , 7 Years ago
Grade 12th Pass
Analytical Geometry> If x and y be reals, then 1/2(x+y+|x-y|)=...
2 Answers
Vedant
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
Approved Last Activity: 7 Years ago
ASh
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
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