The quadratic trinomials
The sequence
Given a square trinomial
In the infinite sequence
Prove that there is an integer in this sequence.
Note that in this problem, square brackets represent integers and curly brackets represent non-integer values or 0.
On the plane coordinate axes with the same but not stated scale and the graph of the function
How can you construct a tangent to this graph at a given point using a compass and a ruler if: a)
The sequence
Prove that if the expression
takes a rational value, then the expression
also takes on a rational value.
Which numbers can stand in place of the letters in the equality
Prove that if the numbers
There are 40 weights of weights of 1 g, 2 g, ..., 40 grams. Of these, 10 weights of even weight were chosen and placed on the left hand side of the scales. Then we selected 10 weights of odd weight and put it on the right hand side of the scales. The scales were balanced. Prove that on one of the bowls of the scales there are two weights with a mass difference of 20 g.