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求解a(1/b+1/c+1/d)+b(1/a+1/c+1/d)+c(1/b+1/a+1/d)+d(1/b+1/c+1/a)的解.条件是a+b+c+d=0
题目详情
求解a(1/b+1/c+1/d)+b(1/a+1/c+1/d)+c(1/b+1/a+1/d)+d(1/b+1/c+1/a)的解.条件是a+b+c+d=0
▼优质解答
答案和解析
a(1/b+1/c+1/d)+b(1/a+1/c+1/d)+c(1/b+1/a+1/d)+d(1/b+1/c+1/a)
=(b+c+d)/a+(a+c+d)/b+(a+b+d)/c+(a+b+c)/d
=-a/a-b/b-c/c-d/d
=-1-1-1-1
=-4
=(b+c+d)/a+(a+c+d)/b+(a+b+d)/c+(a+b+c)/d
=-a/a-b/b-c/c-d/d
=-1-1-1-1
=-4
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