Chứng minh rằng a=b=c nếu có điều kiện sau: (a+b+c)^2 = 3(a^2
Giải thích
a+b+c2=3a2+b2+c2a2+b2+c2+2ab+2bc+2ca=3a2+3b2+3c22a2+2b2+2c2=2ab+2bc+2caa2−2ab+b2+b2−2bc+c2+c2−2ca+a2=0a−b2+b−c2+c−a2=0⇒a−b2=0b−c2=0c−a2=0⇒a=b=c
a+b+c2=3a2+b2+c2a2+b2+c2+2ab+2bc+2ca=3a2+3b2+3c22a2+2b2+2c2=2ab+2bc+2caa2−2ab+b2+b2−2bc+c2+c2−2ca+a2=0a−b2+b−c2+c−a2=0⇒a−b2=0b−c2=0c−a2=0⇒a=b=c