Toán Lớp 8: cm : nếu A2 + B2+C2 = AB + BC+ CA thì A =B=C
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Toán Lớp 8: cm : nếu A2 + B2+C2 = AB + BC+ CA thì A =B=C
Comments ( 2 )
<=>2a^2+2b^2+2c^2=2ab+2bc+2ca
<=>2a^2+2b^2+2c^2-2ab-2bc-2ca=0
<=>(a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)=0
<=>(a-b)^2+(b-c)^2+(c-a)^2=0
->{(a-b=0),(b-c=0),(c-a=0):}->{(a=b),(b=c),(c=a):}->a=b=c
Vậy : a^2+b^2+c^2=ab+bc+ca thì a=b=c