m^2+n^2=a,x^2+y^2=b
=>m²+x²+n²+y²=a+b,a≥0,b≥0
∵m²+x²≥2xy,n²+y²≥2ny
∴2mx+2ny≤a+b
mx+ny≤(a+b)/2
即mx+ny的最大值(a+b)/2