A szöveg csak Firefox böngészőben jelenik meg helyesen. Használja a fenti PDF file-ra mutató link-et a letöltésre. 1. Solve the following equation on the set of real numbers: | | 2. For what positive integers is the value of the following expression also an integer? | | 3. Given that the second coordinates of the points , , are | | determine whether the three points are collinear. 4. What is more favourable: I. If the bank pays annual interest, and the inflation rate is per year, or II. if the bank pays annual interest, and the inflation rate is per year? 5. The first four terms of an arithmetic progression of integers are . Show that can be expressed as the sum of two perfect squares. 6. In an acute triangle , the circle of diameter intersects the line of the altitude from at the points and , and the circle of diameter intersects the line of the altitude from at the points and . Show that the points , , , lie on a circle. 7. The base of a right pyramid is a triangle , the lengths of the sides are , and . , , are points on the corresponding lateral edges, such that , and . Find the angle of the planes of triangle and triangle . 8. Let . Prove that .
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