作业帮因式分解及分式计算1.因式分解1.x^5+x-12.(a+b)(a+b-ab)+(ab-1)(ab+1)2.已只:n为正整数,且n^$-16n^2+100为质数,求n.3.设a=x/(y+z),b=y/(x+z),c=z/(x+y),且x+y+z≠0求a/(a+1)+b/(b+1)+c/(c+1)
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因式分解及分式计算1.因式分解1.x^5+x-12.(a+b)(a+b-ab)+(ab-1)(ab+1)2.已只:n为正整数,且n^$-16n^2+100为质数,求n.3.设a=x/(y+z),b=y/(x+z),c=z/(x+y),且x+y+z≠0求a/(a+1)+b/(b+1)+c/(c+1)
因式分解及分式计算
1.因式分解1.x^5+x-1
2.(a+b)(a+b-ab)+(ab-1)(ab+1)
2.已只:n为正整数,且n^$-16n^2+100为质数,求n.
3.设a=x/(y+z),b=y/(x+z),c=z/(x+y),且x+y+z≠0
求a/(a+1)+b/(b+1)+c/(c+1)
因式分解及分式计算1.因式分解1.x^5+x-12.(a+b)(a+b-ab)+(ab-1)(ab+1)2.已只:n为正整数,且n^$-16n^2+100为质数,求n.3.设a=x/(y+z),b=y/(x+z),c=z/(x+y),且x+y+z≠0求a/(a+1)+b/(b+1)+c/(c+1)
应该没办法分解
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)
3.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
4.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
补充：会拉
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)
(x^2-x+1)*(x^3+x^2-1)
n
x/(y+z)/(x/(y+z)+1)+y/(x+z)/(y/(x+z)+1)+z/(x+y)/(z/(x+y)+1)