(一道数学题)某人用一架不等臂天平称一铁块g的质量,

题目

(一道数学题)某人用一架不等臂天平称一铁块g的质量,
某人用一架不等臂天平称一铁块g的质量,当把铁块放在天平的左盘中时称的质量为400g,把铁块放在天平的右盘中时称的质量为900g.求这一块铁的实际质量.

答案

设铁块重x(g),天平左右臂分别长a,2-a.则,xa = 400(2-a),800 = a(x+400),a = 800/(x+400)900a = x(2-a),900*800/(x+400) = x[2 - 800/(x+400)] = x(2x)/(x+400) = 2x^2/(x+400),900*400 = x^2,x = 30*20 = 600(g)...