Question

求助,1：已知m=x-y，n=xy，试用m，n表示（x³+y³﹚²,求详细过程,

2：当x=-1时,x³＋2x²﹣5x-6=0,请根据这一事实,将x³＋2x²-5x+6分解因式.谢谢,没分了,不好意思,

Answer 1

1. （x³+y³﹚² = (x+y)²(x²-xy+y²)²
(x+y)² =x²+2xy+y² =( x-y)² +4xy = m² + 4n
x²-xy+y² =( x-y)² +xy = m² + n
（x³+y³﹚² = ( m²+4n)(m²+n)²
2. 当x=-1时,x³＋2x²﹣5x-6=0 ,也就是说x+1是x³＋2x²﹣5x-6得分解因式
用x³＋2x²﹣5x-6 除以x+1得 x²+x-6
x²+x-6 = (x-2)(x+3)
故x³＋2x²﹣5x-6=(x+1) (x-2)(x+3)

Answer 2

（x³+y³﹚²
=(x+y)²(x²-xy+y²)²
=[(x-y)²+4xy][(x-y)²+xy]²
=(m²+4n)(m²+n)²
=……

x³＋2x²-5x-6
=x³+1+2x²-5x-7
=(x+1)(x²-x+1)+(2x-7)(x+1)
=(x+1)(x²+x-6)
=(x+1)(x+3)(x-2)

Answer 3

前面的答案差不多了啦。。。