Show that :  A is a square number \(\forall n\in N\) , know :

\(A=1^3+2^3+...+n^3\)  

Give a,b > 0 . Prove that :

a) \(\dfrac{a}{b}+\dfrac{b}{a}\ge2\)

b) \(\dfrac{1}{a}+\dfrac{1}{b}\ge\dfrac{4}{a+b}\)

a) Find x if : |2x + 3| = x + 2

b) Find the smallest value of A = |x - 2006| + |2007 - x| when x change 

Shorter the expression :

A = |x + 0.8| - |x - 25| + 1.9 with a < -0.8 

Give \(\dfrac{2a+b+c+d}{a}=\dfrac{a+2b+c+d}{b}=\dfrac{a+b+2c+d}{c}=\dfrac{a+b+c+2d}{d}\)

Calculator : M = \(\dfrac{a+b}{c+d}+\dfrac{b+c}{d+a}+\dfrac{c+d}{a+b}+\dfrac{a+d}{b+c}\)

Give \(\dfrac{bt-cn}{a}=\dfrac{cm-at}{b}=\dfrac{an-bm}{c}\) (with a,b,c \(\ne\)0) . Demonstrate : \(\dfrac{m}{a}=\dfrac{n}{b}=\dfrac{t}{c}\)

Find three number x,y,z know : \(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\) and 5z - 3x - 4y = 50 

Give \(\Delta ABC\) have 3 acute angle , AB < AC. M is the midpoint of BC. Through MY straight lines perpendicular to the bisectrix of the corner A cuts AB at D, AC at E . 

Demonstrate : BD = CE