Grade 11IIT JEE Entrance Exam
if x2y3 = 6 , [x,y > 0], then least value of 3x+4y=10, true or false?
if x2y3 = 6 , [x,y > 0], then least value of 3x+4y=10, true or false?
1 Answer
Arun
The least value of 3x+4y is 10.
Breaking the term 3x and 4y into 3x/2 , 3x/2 and 4y/3,4y/3,4y/3.
Now we use Arithmetic and Geometric mean to find the least value of the expression.
AM >= GM (Property of AM and GM)
AM of (3x/2,3x/2,4y/3,4y/3,4y/3) >= GM of (3x/2,3x/2,4y/3,4y/3,4y/3)
(3x/2+3x/2+4y/3+4y/3+4y/3)/5 >= (3/2×3/2×4/3×4/3×4/3)
(3x+4y)/5 >=
(3x+4y) >= 2 × 5
(3x+4y) >= 10
Minimum value of 3x+4y = 10
Hence TRUE
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