均值定理,
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均值定理,
均值定理,
均值定理,
6,已知x+2y=2,由均值定理:
3^x+3^2y≥2√(3^x*3^2y)=2√((3)^(x+2y))=2√3^2=3;
7,y=x+1/x+3(x>0),由均值定理:y=x+1/x+3≥2√x*1/x+3=5;
8,㏒x*㏒y=log(x+y)≥Log(2√(xy))
9;因x,y∈R+(正实数),x+2y≥2√(x*2y),所以2√(2xy)≤40,√(2xy)≤80,xy≤3200;
10,y=-2x^2+8x=-2(x^2-4x)=-2(x^2-4x+4-4)=-2(x-2)^2+8
因为:-2(x-2)^2≤0,所以当-2(x-2)^2=0,即x=2时,Ymax=8