若X1满足2X+2^X=5,X2满足2x+2log2(x-2)=5,X1+X2=,

Question

若X1满足2X+2^X=5,X2满足2x+2log2(x-2)=5,X1+X2=,

Answer 1

2x＋2^x=5,即2^(x-1)=5/2-x,
2x+2log2 (x-1)=5 即 log2(x-1)=5/2-x,
∵ y=2^x和y=log2(x)的图像关于y=x对称
∴ y=2^(x-1)与y=log2(x-1)关于y=x-1对称,
则y=5/2-x与y=2^(x-1),y=5/2-x与y=log2(x-1)交点的横坐标即为x1,x2.
∴设交点A(x1,y1),B (x2,y1)
则交点A,B关于y=x-1对称,且在y=5/2-x上
∴ y=x-1和y=5/2-x的交点为(7/4,3/4)
∴x1+x2=(7/4)*2=7/2