Question

求化简：a（a^2+c^2-b^2/2ac + a^2+b^2-c^2/2ab)=b+c

Answer 1

两边同时乘以2得(a^2+c^2-b^2)/c+ (a^2+b^2-c^2)/b=2(b+c)

两边同时乘以bc得a^2×b+c^2×b-b^3+a^2×c+b^2×c-c^3=2b^2×c+2c^2×b

合并同类项后得a^2×b+a^2×c-(b^3+c^3)=bc(b+c)

即a^2(b+c)-(b^2-bc+c^2)=bc(b+c)

即a^2(b+c)=(b^2-bc+c^2+bc)(b+c)

即b^2(c+b)+c^2(c+b)=a^2(c+b)