If a and b are two positive quantities whose sum is λ, then the minimum value of √(1+1a)(1+1b) is
A
λ−2λ
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B
1+2λ
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C
λ−1λ
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D
1+1λ
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Solution
The correct option is B1+2λ Let E=√(1+1a)(1+1b)
E2=1+1a+1b+1ab ⇒E2=1+a+b+1ab⇒E2=1+λ+1ab
Above will be minimum when ab is maximum.
Now we know that if sum of two quantities is constant then their product is maximum when the quantities are equal. ∴a+b=λ⇒a=b=λ2 ∴E2=λ2+4λ+4λ2⇒E2=(λ+2λ)2 ⇒E=λ+2λ⇒E=1+2λ
Hence, The correct answer is option (d)