嵌入不等式

設A＋B＋C＝(2k+1)π
x,y,z∈R
則有
x^2+y^2+z^2>=2yzcosA+2xzcosB+2xycosC
等號成立若且唯若x:y:z=sinA:sinB:sinC
嵌入不等式的等價形式(1)
設A＋B＋C＝(2k+1)π
x,y,z∈R
則有
xy[sin(C/2)]^2+zx[sin(B/2)]^2+yz[sin(A/2)]^2>=(1/4)(2xy+2yz+2zx-x^2-y^2-z^2)
等號成立若且唯若x:y:z=sinA:sinB:sinC
嵌入不等式的等價形式(2)
設A＋B＋C＝(2k+1)π
x,y,z∈R
則有
(x+y+z)^2>=4{xy[cos(C/2)]^2+zx[cos(B/2)]^2+yz[cos(A/2)]^2}
等號成立若且唯若x:y:z=sinA:sinB:sinC