7th International Mathematical Olympiad 1965 Problems & Solutions

A1.  Find all x in the interval [0, 2p] which satisfy:         2 cos x = |v(1 + sin 2x) - v(1 - sin 2x)| = v2. A2.  The coefficients aij of the following equations         a11x1 + a12 x2+ a13 x3 = 0        a21x1 + a22x2 + a23x3 = 0        a31x1 + a32x2 + a33x3 = 0 satisfy the following: (a) a11, a22, a33 are positive, (b) other aij are negative, (c) the sum of the coefficients