超级难的数学竞赛题,高手解答~~

将：a + 1/b = b + 1/c = c + 1/d = d + 1/a = x 转化为方程组： a + 1/b = x b + 1/c = x c + 1/d = x d + 1/a = x 化简得： ab + 1 = bx bc + 1 = cx cd + 1 = dx da + 1 = ax 写成矩阵形式： [a;b;c;d]x=[d,0,0,0;0,a,0,0;0,0,b,0;0,0,0