若M(x,y)在直線x+2y+1=0上移動,則2^x+4^y的最小值是___

熱心網友

因為X+2Y=-1,所以2^(X+2Y)=1/2所以2^X+4^Y=2^X+2^2Y=2根號(2^X*2^2Y)=2根號2^(X+2Y)=根號2

熱心網友

解:由x+2y+1=0得 x=-(2y+1) 2^x+4^y=2^[-(2y+1)]+4^y =2^[-(2y+1)]+(1/2)*[2^(2y+1)]=2[ 2^[-(2y+1)]*2^2y]^(1/2)=2^(1/2) ( 因為a^2+b^2=2ab)

熱心網友

2^x+4^y = 2^x+2^(2y) = 2根號下2^x*2^(2y)=2根號下2^(x+2y)=根號2最小值是根號2