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Question :
If a and b are non-negative real numbers such that a+2b=6, then the average of the maximum and minimum possible values of (a+b) is
Started 1 month ago by Shashank in
Option B
is the correct answer.
Explanatory Answer
a + 2b = 6
a + b = 6 - b
Clearly, the maximum/minimum value of (a + b) depends on the value of b.
Since a and b are positive real numbers,
The minimum value that b can take is 0.
The maximum value that b can take is when a is 0.
0 + 2b = 6
b = 3.
When b = 0; a + b = 6 - b = 6
When b = 3; a + b = 6 - 3 = 3
Therefore, the minimum and maximum values of (a + b) are 3 and 6 respectively.
The average of these extreme values is ( 3 + 6)/2
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