是关于因式分解的``

题目

是关于因式分解的``
1.计算
x×x×x×x+5×x×x-6
(x+y)(x+y+2xy)+(xy+1)(xy-1)
2.已知a×a-5a+1=0(a不等于0),求a×a+1÷(a×a)的值
明天要用,急,

答案

1.
x^4+5x^2-6
=(x^2+6)(x^2-1)
=(x^2+6)(x-1)(x+1)
2.
(x+y)(x+y+2xy)+(xy+1)(xy-1)
=(x+y)^2+2xy(x+y)+(xy+1)(xy-1)
=(x+y+xy+1)(x+y+xy-1)
=[(x+xy)+(y+1)](x+y+xy-1)
=[x(y+1)+(y+1)](x+y+xy-1)
=(x+1)(y+1)(x+y+xy-1).
3.

a不等于0,a^2-5a+1=0,两边同时除以a,
得：a-5+(1/a)=0,即a+(1/a)=5
又因为a^2+1/a^2=(a+1/a)^2-2
所以a^2+1/a^2=5^2-2=23
回答完毕!
(a^2+1)/(a^2)