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题目已知a,b,c是满足4abc(a+b+c)=(a+b)2(a+c)2的正实数,求证:a(a+b+c)=bc.这是2012年美国数学奥林匹克竞赛试题,它是一个条件等式的证明问题,先来研究它的代数证明.证明1(代数法)
It is known that a, b and c are positive real numbers that satisfy 4abc (a + b + c) = (a + b) 2 (a + c) The 2012 American Mathematical Olympiad exam, which is a proof of the conditional equation, first studies its algebraic proof. Proof 1 (Algebra)