Question

cho a+b+c=2p. cmr :^{\(2bc+b^2+c^2-a^2=4p\left(p-a\right)\)}

Answer 1

Xét \(VP=4p.\left(p-a\right)=2p.2.\left(p-a\right)=2p.\left(2p-2a\right)=\left(a+b+c\right)\left(b+c-a\right)\)

\(ab+ac-a^2+b^2+bc-ab+bc+c^2-ac=2bc+b^2+c^2-a^2=VT\)

Vậy ta có đpcm

Answer 2

2bc+b^2+c^2-a^2=(b+c)^2-a^2=(b+c-a)(b+c+a)=(2p-a-a)2p=(2p-2a)2p=2.2p(p-a)=4p(p-a)