It is known that a · B · C is the three sides of △ ABC and satisfies the equation A & sup2; + B & sup2; + C & sup2; - AB AC BC = 0 Prove that △ ABC is an equilateral triangle

Lillillele,
∵a^2＋b^2＋c^2－ab－ac－bc＝0
∴2a^2＋2b^2＋2c^2－2ab－2ac－2bc＝0
a^2－2ab＋b^2＋b^2－2bc＋c^2＋a^2－2ac＋c^2＝0
That is, (a-b) ^ 2 + (A-C) ^ 2 + (B-C) ^ 2 = 0
∴a＝b＝c
The ABC is an equilateral triangle

It is known that a · B · C is the three sides of △ ABC and satisfies the equation A & sup2; + B & sup2; + C & sup2; - AB AC BC = 0 Prove that △ ABC is an equilateral triangle

It is known that a · B · C is the three sides of △ ABC and satisfies the equation A & sup2; + B & sup2; + C & sup2; - AB AC BC = 0 Prove that △ ABC is an equilateral triangle

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