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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....

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....

Grade:

1 Answers

Prudhvi teja
83 Points
11 years ago

Dear 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}

as desired.

Please feel free to post as many doubts on our discussion forum as you can.we will get you the answer and detailed  solution very  quickly.

All the best.

Regards,
Askiitians Experts
Prudhvi Teja

 

 


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