已知a＞0,b＞0,a+b=1,求证:√(a+1/2)+√(b+1/2)≤2.
热心网友
a+b=1(a+1/2)(b+1/2)<=1(√(a+1/2)+√(b+1/2))^2=a+1/2+b+1/2+2√(a+1/2)(b+1/2)≤2+2*1=4故:√(a+1/2)+√(b+1/2)≤2.
已知a＞0,b＞0,a+b=1,求证:√(a+1/2)+√(b+1/2)≤2.
a+b=1(a+1/2)(b+1/2)<=1(√(a+1/2)+√(b+1/2))^2=a+1/2+b+1/2+2√(a+1/2)(b+1/2)≤2+2*1=4故:√(a+1/2)+√(b+1/2)≤2.