chứng minh đẳng thức: (y- a)(y - b)+ (y- b)(y - c)+ (y - c)(y- a) = ab+ bc + ca biết rằng a+b+c = 1,5y
[tex](y- a)(y - b)+ (y- b)(y - c)+ (y - c)(y- a) [/tex]
=[tex]y^2-ay-by+ab-y^2-by-cy+bc+y^2-cy-ay+ac[/tex]
=[tex]3y^2-2ay-2by-2cy+ab+bc+ac[/tex]
=[tex]3y^2-2y(a+b+c)+ab+bc+ac[/tex] . Thay a+b+c=1,5y
=[tex]3y^2-2.1,5y+ab+bc+ca[/tex]
=[tex]3y^2-3y^2+ab+bc+ca[/tex]
=[tex]ab+bc+ca[/tex] (đpcm)