Algebra> application of am n gm...
i mm class 11th now n i just wanna ask dat how do u cum 2 know dat u hv 2 apply the concepts of a.m. n g.m. in various types of questions...?????????? i.e. am less than equal to gm. kindly illustrate with an example....
1 AnswersDear priyanka
A.M < G.M
Take two terms, x1 and x2, and since (by our assumption) not all terms are equal, we have:
![\begin{align} x_1 & \ne x_2 \\[3pt] x_1 - x_2 & \ne 0 \\[3pt] \left( x_1 - x_2 \right) ^2 & > 0 \\[3pt] x_1^2 - 2 x_1 x_2 + x_2^2 & > 0 \\[3pt] x_1^2 + 2 x_1 x_2 + x_2^2 & > 4 x_1 x_2 \\[3pt] \left( x_1 + x_2 \right) ^2& > 4 x_1 x_2 \\[3pt] \Bigl( \frac{x_1 + x_2}{2} \Bigr)^2 & > x_1 x_2 \\[3pt] \frac{x_1 + x_2}{2} & > \sqrt{x_1 x_2} \end{align}](http://upload.wikimedia.org/math/4/c/f/4cf36911301e4ae4ed164b8e101e66b1.png)
as desired.
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