Question

已知x.y属于R.求证,(x²+y²)/2≥【(x+y)/2】²

Answer 1

x²+y²≥2xy

两边同时加上(x²+y²),则有

2(x²+y²)≥2xy+x²+y²

2(x²+y²)≥(x+y)²

两边同时除以4,则有

(x²+y²)/2≥(x+y)²/4

即(x²+y²)/2≥[(x+y)/2]²

证毕.