Min of Sum of 3 Terms

Algebra Level pending

Let $x > 0$ and $y > 0$ , and let $m$ be the minimum value of $4 x^2 + \frac{y}{2x} + \frac{4}{xy}$ . Let $a$ and $b$ be the values of $x$ and $y$ , respectively, that yield the minimum value $m$ . What is the value of $m + ab ?$

10

4

6

8

1 solution

Arijit ghosh Dastidar
Feb 13, 2015

using am gm inequality the minimum value of the function is 6, so m=6 for the minimum value the terms should be equal, so, the value of y, b comes out to be (8 )^1/2 x, a comes out to be (2)^ -1/2 so, m+ab= 6+ 2= 8

simply genius!! pl. use LaTeX next time...

Sarthak Rath - 6 years, 3 months ago

Min of Sum of 3 Terms

1 solution

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