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प्रश्न
The minimum value of 4x + 41–x, x ∈ R, is ______.
विकल्प
2
4
1
0
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उत्तर
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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