Question

因式分解及分式计算

⒈因式分解:①x＾5+x-1
②(a+b)(a+b-2ab)+(ab-1)(ab+1)

⒉已知n为正整数，且n＾4-16n＾2+100为质数，求n？

⒊设a=x/(y+z)，b=y/(z+x)，c=z/(x+y),且x+y+z≠0,
求a/(a+1)+b/(b+1)+c/(c+1)

Answer 1

⒈①不懂
②(a+b)(a+b-2ab)+(ab-1)(ab+1)= (a+b)^2-2ab(a+b)+(ab)^2-1=(a+b-ab)^2-1=(a+b-ab+1)(a+b-ab-1)
2.n=3,17,27,37,47,57,67,87,97,107,117,127,137,147,157,167,177,187,197,207,217和227.
⒊把"a=x/(y+z)，b=y/(z+x)，c=z/(x+y)"代入就可以了,过程不难.答案是"1".
(施舍点分吧!)

Answer 2

1.:① x^5+x-1
=x^5-x^4+x^3+x^4-x^3+x^2-x^2+x-1
=(x^5-x^4+x^3)+(x^4-x^3+x^2)-(x^2-x+1)
=(x^3+x^2-1)(x^2-x+1)
②。(a+b)(a+b-ab)+(ab-1)(ab+1)
=(a+b)(1-ab)-(1-ab)(1+ab)
=(1-ab)(a+b-ab-1)
=(1-ab)(a-1)(1-b)
2.n^4-16n^2+100
=(n^2-6n+10)(n^2+6n+10)
n^4-16n^2+100为质数
n^2-6n+10=1 or n^2+6n+10=1
n=3 or n=-3
3.a=x/(y+z),a+1=(x+y+z)/(y+z)
a/(a+1)=x/(x+y+z)
b/(b+1)=y/(x+y+z)
c/(c+1)=z/(x+y+z)
a/(a+1)+b/(b+1)+c/(c+1)=1

(参考资料也是我答的)