If x,y are real numbers such that x^2+y^2+2 ≤ 2x+2y , find the value of x+y

Show that the inequality \dfrac{6^n}{n!}\leq \dfrac{6^5}{5!}\times \dfrac{6}{n} is true

In △ABC , medians BE and CD are perpendicular to each other and intersect at Z . If BE = 8 cm, CD = 12 cm, what is the area of △ABC ?

Factor the expression (x^2+x)(x^2+x-1)-2

Find the limit of the progression

\lim\limits_{n\to \infty} \sqrt{n^2+n}-n