(1)设P(x)=1/2[f(x1-1)+f(x2-1)] - f[(x1+x2-2)/2]=1/2[ln(x1)+ln(x2)]-ln[(x1+x2)/2]=ln[2√(X1·X2)/(x1+x2)],易知(x1+x2)²≥4x1·x2,∴2√(X1·X2)/(x1+x2)≤1,即P(x)≤0
(2)求证什么?望楼主明确……
(1)设P(x)=1/2[f(x1-1)+f(x2-1)] - f[(x1+x2-2)/2]=1/2[ln(x1)+ln(x2)]-ln[(x1+x2)/2]=ln[2√(X1·X2)/(x1+x2)],易知(x1+x2)²≥4x1·x2,∴2√(X1·X2)/(x1+x2)≤1,即P(x)≤0
(2)求证什么?望楼主明确……