已知a+b+c=0,求b²-c²/a+c²-a²/b+a²-b²/c的值
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已知a+b+c=0,求b²-c²/a+c²-a²/b+a²-b²/c的值
已知a+b+c=0,求b²-c²/a+c²-a²/b+a²-b²/c的值
已知a+b+c=0,求b²-c²/a+c²-a²/b+a²-b²/c的值
a+b+c=0
a+b=-c
a+c=-b
b+c=-a
b²-c²/a+c²-a²/b+a²-b²/c
=b²-c²/[-(b+c)]+c²-a²/[-(a+c)]+a²-b²/[-(a+b)]
=c-b+a-c+b-a
=0
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因为a+b+c=0
所以a+b=-c
b+c=-a
a+c=-b
所以b^2-c^2/a+c^2-a^2/b^2+a^2-b^2/c
=(b+c)(b-c)/a+(a+c)(c-a)/b+(a+b)(a-b)/c
=-a(b-c)/a+(-b)(c-a)/b+(-c)(a-b)/c
=-(b-c)-(c-a)-(a-b)
=-b+c-c+a-a+b
=0
所以b^2-c^2/a+c^2-a^2/b+a^2-b^2/c的值是0