Problem: Draw the region of points in the plane, which satisfy . Solution: region will bounded by lines , , & . Why is that? First note that \( |x| \le 1 \) implies: Similarly, if we demand \( |y| \le 1 \) (the double shaded zone). Now if we want \( |y| \le |x|...

problem: For , show that , where is a positive integer. solution: Now to prove \( ( \dagger) \) we observe: But Now this follows directly from AM-GM...

Problem : If a, b and c are the lengths of the sides of a triangle ABC and if \( p_1 , p_2 \) and \( p_3 \) are the lengths of the perpendiculars drawn from the circumcentre onto the sides BC, CA and AB respectively, then show that . Solution : Let O be the circum...

Problem : Let be polynomials in , each having all integer coefficients, such that . Assume that is not the zero polynomial. Show that and Solution : As are integer coefficient polynomials so gives integer values at integer points. Now as is not zero polynomial for...

Problem : Suppose there are teams playing a round robin tournament; that is, each team plays against all the other teams and no game ends in a draw.Suppose the team loses games and wins games.Show that = Solution : Each team plays exactly one match against each other...