[ 東京工業大学 1957 年 解析Ⅰ １ ]
, ,
1 1 1
b c c a a b
x y z
bc ca ab
− − −
= = =
+ + +
なるとき，x+ + −y z xyz をなるべく簡単にせよ。x+ + −y z xyz
1 1 1 1 1 1
b c c a a b b c c a a b
bc ca ab bc ca ab
− − − − − −
= + + − ⋅ ⋅
+ + + + + +
( )(1 ) ( )(1 )
(1 )(1 ) 1 1 1 1
b c ca c a bc a b b c c a a b
bc ca ab bc ca ab
− + + − + − − − −
= + − ⋅ ⋅
+ + + + + +
2 2
(1 )(1 ) 1 1 1 1
b c abc c a c a bc abc a b b c c a a b
bc ca ab bc ca ab
− + − + − + − − − − −
= + − ⋅ ⋅
+ + + + + +
( )(1
2)
(1 )(1 ) 1 1 1 1
a b c a b b c c a a b
bc ca ab bc ca ab
− − + − − − −
= + − ⋅ ⋅
+ + + + + +
(1
2)(1 ) (1 )(1 )
( )
(1 )(1 )(1 ) 1 1 1
c ab bc ca b c c a a b
a b bc ca ab bc ca ab
− + + + + + − − −
= − − ⋅ ⋅
+ + + + + +
2 2 2
(1 ) 1
( )
(1 )(1 )(1 ) 1 1 1
ab c abc ca bc abc b c c a a b
a b bc ca ab bc ca ab
− + + + + + + + − − −
= − − ⋅ ⋅
+ + + + + +
( )( )
( )
(1 )(1 )(1 ) 1 1 1
b c c a b c c a a b
a b bc ca ab bc ca ab
− − − − −
= − − ⋅ ⋅
+ + + + + +
=0
