Solve the system of equation for (x,y)∈R {√x2+y2+√(x−4)2+(y−3)2=53x2+4xy=24 Explain your answer
2017 Azerbaijan Junior National Olympiad
For all n>1 let f(n) be the sum of the smallest factor of n that is not 1 and n . The computer prints f(2),f(3),f(4),... with order:4,6,6,... ( Because f(2)=2+2=4,f(3)=3+3=6,f(4)=4+2=6 etc.). In this infinite sequence, how many times will be 2015 and 2016 written? (Explain your answer)
Show that (x+y+z)23≥x√yz+y√zx+z√xy for all non-negative reals x,y,z.
A Rhombus and an Isosceles trapezoid that has same area is drawn in the same circle's outside. Compare their acute angles (explain your answer)
A student firstly wrote x=3 on the board. For each procces, the stutent deletes the number x and replaces it with either (2x+4) or (3x+8) or (x2+5x). Is this possible to make the number (2017+2016) on the board? (Explain your answer) NoteThis type of the question is well known but I am going to make a collection so,