x1满足2x＋2^x=5,x2满足2x+2log2 (x-1)=5 ,则x1＋x2＝

题目

x1满足2x＋2^x=5,x2满足2x+2log2 (x-1)=5 ,则x1＋x2＝
2009辽宁数学第12题

答案

x+2^(x-1)=2.5,x+log2(x-1)=2.5,其中y=2^(x-1)与y=log2(x-1)关于y=x-1对称,y=2.5-x与前面指数,对数曲线交点即为x1,x2.x1+x2为y=2.5-x,y=x-1交点横坐标2倍即3.5