>>564
x=b+c-a,y=c+a-b,z=a+b-cとおくとx>0,y>0,z>0
左辺*4={(y+z)^2}x+{(z+x)^2}y+{(x+y)^2}z
=(y^2+z^2+2yz)x+(z^2+x^2+2zx)y+(x^2+y^2+2xy)z
=(y^2+z^2)x+(z^2+x^2)y+(x^2+y^2)z+6xyz
右辺*8=3(y+z)(z+x)(x+y)
=3{(x^2)y+(x^2)z+(y^2)x+(y^2)z+(z^2)x+(z^2)y+2xyz}
=3(y^2+z^2)x+3(z^2+x^2)y+3(x^2+y^2)z+6xyz

右辺*8-左辺*8=(y^2+z^2)x+(z^2+x^2)y+(x^2+y^2)z-6xyz
=(y^2+z^2)x-2xyz+(z^2+x^2)y-2xyz+(x^2+y^2)z-2xyz
={(y-z)^2}x+{(z-x)^2}y+{(x-y)^2}z≧0