If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum values of (a + b) is:
Explanation:
Given, a + 2b = 6. ⇒ a + b = 6 - b
∴ (a + b) will be maximum when b is least. Least value of b can be 0, since b cannot be negative. ⇒ (a + b)max = 6
∴ (a + b) will be minimum when b is highest. Highest value of b can be 3, since a cannot be negative. ⇒ (a + b)min = 3
⇒ Average of highest and lowest values of (a + b) = 3+62 = 4.5
Hence, option (b).
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