Recent content by Schalk21

Is correct to say that ##\sqrt {(x_{1,2})^2} = x_{1,2}## because ##x_{1,2} \geq 0##, so ## \frac {(x_1)^2 + (x_2)^2} {2} \geq \sqrt {(x_1 × x_2)^2}## ? Or in order to avoid any type of problem ## (x_1)^2+(x_2)^2 + 2 (x_1)(x_2) \geq 4(x_1)(x_2), (x_1+x_2)^2 \geq 4(x_1)(x_2)## and taking the...

Sorry I don't understand "the rest of the argument" You are right, I'm not English so probably i had to use "simple", nothing is "trivial" Yes, I' m an high schooler respect to my school system. I made that question after the discussion with etotheipi who suggested the "scalar field method" to...

Problem 11 Let's recall the simplest AM-GM inequality: for two non-negative numbers ##x_1## and ##x_2## , $$\frac {x_1+x_2} {2} \geq \sqrt {x_1×x_2}$$. The equality holds when ##x_1=x_2##. Method 1: This method is the simplest and classical one. It is based on the fact that ##(x_1-x_2)^2 \geq...

Yes perfect, I didn't know this concept but now it's clear. Thank you so much!

Well, the first method seems really clever but it's beyond my knowledge. I think I can learn and understand the second one.

Yes, you are right. I'll try to work on other methods as you suggested

Problem 12: In a xOy plane, Let's consider the unit circle of equation ##x^2+y^2=1##. Each point of this curve ##(x_0 ; y_0)## has coordinates ##(\cos \alpha ; \sin \alpha)## for a simple definition of cosine and sine, where alpha is the angle between the radius and the positive verse of x-axis...