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Question
The minimum value of 4x + 41–x, x ∈ R, is ______.
Options
2
4
1
0
Solution
The minimum value of 4x + 41–x, x ∈ R, is 4.
Explanation:
We know that AM ≥ GM
∴ `(4^x + 4^(1 - x))/2 ≥ sqrt(4^x * 4^(1 - x))`
⇒ `4^x + 4^(1 - x) ≥ 2sqrt(4^(x + 1 - x))`
⇒ `4^x + 4^(1 - x) ≥ 2 * 2`
⇒ `4^x + 4^(1 - x) ≥ 4`
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