Find x know :

(x - 1)⁴ = (x - 1)⁶

Give rectangle ABCD , connect C to any point E on the BD diagonal , on ray EC , choose F so that EF = EC. Draw FH and FK perpendicular to AB and AD . Prove that :

a) Quadrilateral AHFK is a rectangle 

b) AF parellel to BD and KH parellel to AC

c) Three points E,H,K are straight .

Find the smalest value .

a) A = x² + 3x + 7

b) B = 2x² + 9y² - 6xy - 6x - 12y + 2004 

Polynomial analysis into factor multiplication :

A = (x² + y²)³ + (z² - x²)³ - (y² + z²)³

Give a + b = 1

Find value of M know :

M = 2(a³ + b³) - 3(a² + b²)

Give a + b + c = 0

Prove that : 

a³ + b³ + c³ = 3abc 

Give a,b,c are positive real numbers and a² + b² + c² = 3

Prove that |a| + |b| + |c| - abc \(\le\) 4

Give a,b,c \(\ge\) 0

Prove that : \(\left(ab+bc+ca\right)^2\ge3abc\left(a+b+c\right)\)

1) Prove if the sum of x,y,z positive so :

\(x+y+z\ge3xyz\)

2) Give x,y are positive real number and x + y = 16.

Find the smallest value of \(M=\dfrac{9}{xy}+\dfrac{17}{x^2+y^2}\)

Given three number a,b,c know :

0 \(\le\) a \(\le\) b + 1 \(\le\) c + 2 and a + b + c = 1 .

Find the smallest value of c .