企源知识库

证明行列式
|xyx+y|
|yx+yx|
|x+yxy|
=-2(x³+y²)
【正确答案】：证明： |x y x+y| |y x+y x| |x+Y x y| = |2x+2y y x+y| |2x+2y x+y x| |2x+2y x y| =2(x+y) |1 y x+y| |1 x+y x| |1 x y| =2(x+y) |1 y x+y| |0 x -y| |0 x-y -x| =2(x+y)(-x²+xy-y²) =-2(x³+y³)