(1)由3x²+xy-2y²=0得:
(x+y)(3x-2y)=0
x=-y或 x=2y/3
x/y-y/x-(x²+y²)/xy
=(x²-y²)/xy-(x²+y²)/xy
=-2y²/xy=-2y/x
把 x=-y或 x=2y/3代入上式有
-2y/x =2或-3
所以x/y-y/x-(x²+y²)/xy的值的2或-3
(2)(a+b-c)/c=(a-b+c)/b=(-a+b+c)/a
=(a+b)/c=(a+c)/b=(b+c)/a
=〔(a+b)+(a+c)+(b+c)〕/(c+b+a)(等式的分子分母分别相加,等式的值不变)
=2
所以(a+b)(b+c)(c+a)/abc
=〔(a+b)/c〕〔(a+c)/b〕〔(b+c)/a〕
=2×2×2
=8