.已知非零实数x,y满 x/y+y/x+2xy=x^2-y^2,求x^2加y^2的最小值答:设u=x^2+y^2,v=xy,则 x/y+y/x+2xy=x^2-y^2 变为(x^2+y^2)/(xy)+2xy=x^2-y^2,平方得u^2/v^2+4u+4v^2=u^2-4v^2,整理得8v^4+(4u-u^2)v^2+u^2=0,u,v为实数,所以(4u-u^2)^2-32u^2=u^2(u^2-8u-16)≥0,u≥0,所以u>0时u^2-8u-16≥0,解...
已知非零实数a,b,c,满足3^a=6^b=24^c答:2^a=3,2^b=6,2^c=12 所以 a=log2(3),b=log2(6),c=log2(12)2b-(a+c)=2log2(6)-log2(3)-log2(12)=log2(36)-log2(36)=0 所以 a,b,c成等差数列 而b^2不等于ac,所以不是等比数列.