1.1/a+1/b+1/c =(a+b+c)/a+(a+b+c)/b+(a+b+c)/c =3+b/a+c/a+a/b+c/b+a/c+b/c =3+(b/a+a/b)+(a/c+c/a)+(c/b+b/c) b/a+a/b>=2*根号[(b/a)*(a/b)]=2 同理 c/a+a/c>=2 c/b+b/c>=2 所以 1/a+1/b+1/c>=92.(1/a-1)(1/b-1)(1/c-1)=[(a+b+c)/a-1][(a+b+c)/b-1][(a+b+c)/c-1]=(b/a+c/a)(a/b+c/b)(a/c+b/c)=(b+c)(c+a)(a+b)/abcb+c>=2(bc)^0.5c+a>=2(ac)^0.5a+b>=2(ab)^0.5带入整理得(1/a -1)(1/b -1)(1/c -1)≥8 2^x+2^y=2^x+2^(x^2)>=2(2^x*2^(x^2))=2^[(x^2+x+2)/2]所以 ㏒2 (2x+2y)>=log2{2^[(x^2+x+2)/2]}=(x^2+x+2)/2>=7/8
