若X1满足2X+2^X=5,X2满足2X+2log2(X-1)=5,(2log2(x-1)中(x-1)前的2为底数) 求X1+X2
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若X1满足2X+2^X=5,X2满足2X+2log2(X-1)=5,(2log2(x-1)中(x-1)前的2为底数) 求X1+X2
若X1满足2X+2^X=5,X2满足2X+2log2(X-1)=5,(2log2(x-1)中(x-1)前的2为底数) 求X1+X2
若X1满足2X+2^X=5,X2满足2X+2log2(X-1)=5,(2log2(x-1)中(x-1)前的2为底数) 求X1+X2
原来两方方程可变为
2^(x-1)=2.5-x
log2(x-1)=2.5-x
设函数f1(x)=2^(x-1)
f2(x)=log2(x-1)
f3(x)=2.5-x
则X1与X2分别是f3(x)与f1(x)和f2(x)的交点的横坐标,
因为f1(x)=2^(x-1)与f2(x)=log2(x-1)关于y=x-1对称,f3(x)=2.5-x...
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原来两方方程可变为
2^(x-1)=2.5-x
log2(x-1)=2.5-x
设函数f1(x)=2^(x-1)
f2(x)=log2(x-1)
f3(x)=2.5-x
则X1与X2分别是f3(x)与f1(x)和f2(x)的交点的横坐标,
因为f1(x)=2^(x-1)与f2(x)=log2(x-1)关于y=x-1对称,f3(x)=2.5-x关于y=x-1对称
所以(X1,y1)与(X2,y2)关于y=x-1对称
因为f3(x)=2.5-x与y=x-1的交点是(1.75,0.75)
所以(X1,y1)与(X2,y2)关于(1.75,0.75)对称
所以x1+x2=2*1.75=3.5
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