:
M=bc(y−z)^2+ca(z−x)^2+ab(x−y)^2=>A=bc(y−z)2+ca(z−x)2+ab(x−y)2
Khai triển các bình phương và gom các nhân tử chung :
A=(ab+ac)x2+(ab+bc)y^2+(bc+ac)z^2−2abxy−2bcxy−2acxyM=(ab+ac)x2+(ab+bc)y^2+(bc+ac)z^2−2abxy−2bcxy−2acxy
=[(ab+ac)x2+a^2x^2+(ab+bc)y^2+b^2y^2+(bc+ac)z^2+c^2z^2]−=[(ab+ac)x2+a^2x^2+(ab+bc)y2+b^2y62+(bc+ac)z2+c2z2]−(a^2x^2+b^2y^2+c^2z^2+2ab+2aczx+2bcyz)(a^2x^2+b^2y^2+c^2z^2+2ab+2aczx+2bcyz)
=(a+b+c)(ax^2+by^2+cz^2)−(ax+by+cz)^2=(a+b+c)(ax^2+by^2+cz^2)−(ax+by+cz)^2
=(a+b+c)(ax^2+by^2+cz^2)=(a+b+c)(ax^2+by^2+cz^2) ( vì ax+by+cz=0,ax+by+cz=0 )
=>A=a+b+c
