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!!!

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.