Question

x,y,z∈R⁺,x+y+z=1,下列各式正确的是……(　　)

A.x²+y²+z²≥1

B.x²+y²+z²≥2

C.xy+yz+xz≥

D.x²+y²+z²≥

Answer 1

解析:由于x²+y²+z²≥xy+yz+xz,又1=(x+y+z)²=x²+y²+z²+2(xy+yz+xz),?

∴3(x²+y²+z²)≥1.则x²+y²+z²≥.故选D.?

答案:D