Question

# If a and b are two positive quantities whose sum is λ, then the minimum value of √(1+1a)(1+1b) isλ−1λλ−2λ1+1λ1+2λ

Solution

## The correct option is D 1+2λE2=1+1a+1b+1ab=1+a+b+1ab=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=(λ+2λ)2 ∴E=λ+2λ=1+2λ⇒(d)

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