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

Question

UPSC Quizroom · Accepted Answer

a and b are non-negative real numbers and
a + 2b = 6

We rewrite a in terms of b:
a = 6 − 2b

Since a ≥ 0,
6 − 2b ≥ 0 ⇒ b ≤ 3
Also b ≥ 0, so 0 ≤ b ≤ 3

Now evaluate a + b:
a + b = (6 − 2b) + b = 6 − b

When b = 0:
a + b = 6 − 0 = 6 (maximum)

When b = 3:
a + b = 6 − 3 = 3 (minimum)

Average of maximum and minimum:
(6 + 3) / 2 = 4.5

Answer: 4.5

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