1. Determine all pairs of integer (x;y) such that \(2xy^2+x+y+1=x^2+2y^2+xy\)

2. Let a,b,c satisfies the conditions

           \(\hept{\begin{cases}5\ge a\ge b\ge c\ge0\\a+b\le8\\a+b+c=10\end{cases}}\)

      Prove that \(2a^2+b^2+c^2\le38\)

3. Let a nad b satis fy the conditions

           \(\hept{\begin{cases}a^3-6a^2+15a=9\\b^3-3b^2+6b=-1\end{cases}}\) 

 Find the value of\(\left(a-b\right)^{2014}\) ?

4. Find the smallest positive integer n such that the number \(2^n+2^8+2^{11}\) is a perfect square.

Lesson 1: analyzing the polynomial factors.

Notes + 2 x-1
x 3 + 6x2 + 11x + 6
x 4 + 2 x 2-3
AB + ac + b2 + 2bc + c2
A3-b3 + c3 + 3abc
Lesson 2: for functions: 

search conditions of x to A means.
A shortening.
Computer x to A < 1.
Post 3: prove the inequality:

For a + b + c = 0. Prove that: a3 + b3 + c3 = 3abc.
For a, b, c are the sidelengths of the triangle. Proof that:


Prove that x 5 + y5 ≥ x4y + xy4 with x, y ≠ 0 and x + y ≥ 0
Lesson 4: solve the equation:

x 2-3 x + 2 + | x-1 | = 0


Lesson 5: find the largest and smallest value (if any)

A = x 2-2 x + 5
B =-2 x 2-4 x + 1.
C = 
Lesson 6: calculate the value of expression.

Know a – b = 7 feature: A = (a + 1) a2-b2 (b-1) + ab-3ab (a-b + 1)
For three numbers a, b, c is not zero catches up deals for equality: 
Computer: P = 

Article 7: proof that

8351634 + 8241142 divisible 26.
A = n3 + 6n2-19n-24 divisible by 6.
B = (10n-9n-1) divisible 27 with n in N *.
Article 8:

In the motorcycle race three cars depart at once. The second car in a one-hour run slower than the first car 15 km and 3 km third cars. rapidly should the destination more slowly the first car 12 minutes and the third car earlier today. No stops along the way. Calculate the speed of each car, race distance and the time each car

1) ABC is a triangle where M is the midpoint of segment BC.

MD and ME are two bisectors of triangles AMB and AMC respectively.

If AM= m; BC = a . Then DE = ???

2)\(\dfrac{1}{\left(x+29\right)^2}+\dfrac{1}{\left(x+30\right)^2}=\dfrac{5}{4}\)

What is the product of all real solutions to the equation above?

3) The sum of all possible natural numbers n such that

\(n^2+n+1589\) is a perfect square is.....

4) Given that x is a positive integer such that x and x+99 are perfect squares

The sum of integer x is ...

5)The operation @ on two numbers produces a number equal to their sum minus 2. The value of

(...((1@2)@3....@2017)

6) Given f(x)=\(\dfrac{x^2}{2x-2x^2-1}\)

=> \(f\left(\dfrac{1}{2016}\right)+f\left(\dfrac{2}{2016}\right)+f\left(\dfrac{3}{2016}\right)+...+f\left(\dfrac{2016}{2016}\right)\)

Các bn giúp mk vs >>> tks nha!!!