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Question

If a and b are two positive quantities whose sum is λ, then the minimum value of (1+1a)(1+1b) is
  1. λ1λ
  2. λ2λ
  3. 1+1λ
  4. 1+2λ


Solution

The correct option is D 1+2λ
E2=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=λa=b=λ2
E2=λ2+4λ+4λ2=(λ+2λ)2
E=λ+2λ=1+2λ(d)

 

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