Minimum value of a linear identity

Algebra Level 3

What is the Local-Minimum value of 4x+9y

if

xy = 64 , and x > 0 , y > 0


The answer is 96.

Vijay Simha by Vijay Simha , 47, USA

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1 solution

Curtis Clement
Aug 3, 2015

Using AM-GM: 4 x + 9 y ≥ + 2 36 x y = 2 × 6 × 8 = 96 \ 4x+9y \geq\ +2 \sqrt{36xy} = 2 \times\ 6 \times\ 8 = 96 (with equality when 4x = 9y). Hence, 96 is the local minimum assuming that x,y > 0

1 Helpful 0 Interesting 0 Brilliant 0 Confused

That is an excellent use of the AM>GM inequality.

Vijay Simha - 5 years, 10 months ago

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