wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If a and b are two positive quantities whose sum is λ, then the minimum value of (1+1a)(1+1b) is

A
λ1λ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
λ2λ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1+1λ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1+2λ
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
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)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Inequalities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon