Question
If a and b are two positive quantities whose sum is λ, then the minimum value of √(1+1a)(1+1b) is
Answer: Option D
:
D
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=λ⇒a=b=λ2
∴E2=λ2+4λ+4λ2=(λ+2λ)2
∴E=λ+2λ=1+2λ⇒(d)
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:
D
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=λ⇒a=b=λ2
∴E2=λ2+4λ+4λ2=(λ+2λ)2
∴E=λ+2λ=1+2λ⇒(d)
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