已知A(X1,Y2)B(X2,Y2)C(X3,Y3)在y=2^x 上 X1+2X2+3X3=1 则Y1+Y2^2+Y3^3的最小值

x=log2(y)
则X1+2X2+3X3
=log2(y1)+2log2(y2)+3log2(y3)
=log2(y1)+log2(y2^2)+log2(y3^3)
=log2(y1y2^2y3^3)=1
所以y1y2^2y3^3=2
且y1>0,y2>0,y3>0
所以y1+y2^2+y3^3≥3(y1y2^2y3^3)^(1/3)=3(2)^(1/3)