已知实数a,b,m,n满足a^2+b^2=1,m^2+n^2=1求证:am+bn
问题描述：
已知实数a,b,m,n满足a^2+b^2=1,m^2+n^2=1求证:am+bn
答
a^2+b^2+m^2+n^2=2>=2am+2bn am+bn
答
因为a,b,m,n均为实数,则有(a-m)^2>=0,(b-n)^2>=0,
则有a^2+m^2-2am>=0,b^2+n^2-2bn>=0,
两式相加：a^2+m^2+b^2+n^2>=2am+2bn
因为a^2+b^2=1,m^2+n^2=1,
所以2am+2bn