1.分解因式:a^4+2a^3b+3a^2b^2+2ab^3+b^42.对於任意自然数n,有f(n)=1/{[三次根号(n^2+2n+10+三次根号(n^2-1)+三次根号(n^-2n+1)]},则f(1)+f(3)+f(5)+…… +f(999)=?已知a、b、c、d是正整数,且b/a=(4d-7)/c,(b+1)/
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![1.分解因式:a^4+2a^3b+3a^2b^2+2ab^3+b^42.对於任意自然数n,有f(n)=1/{[三次根号(n^2+2n+10+三次根号(n^2-1)+三次根号(n^-2n+1)]},则f(1)+f(3)+f(5)+…… +f(999)=?已知a、b、c、d是正整数,且b/a=(4d-7)/c,(b+1)/](/uploads/image/z/1343803-67-3.jpg?t=1.%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%EF%BC%9Aa%5E4%2B2a%5E3b%2B3a%5E2b%5E2%2B2ab%5E3%2Bb%5E42.%E5%AF%B9%E6%96%BC%E4%BB%BB%E6%84%8F%E8%87%AA%E7%84%B6%E6%95%B0n%2C%E6%9C%89f%EF%BC%88n%EF%BC%89%3D1%2F%7B%5B%E4%B8%89%E6%AC%A1%E6%A0%B9%E5%8F%B7%EF%BC%88n%5E2%2B2n%2B10%2B%E4%B8%89%E6%AC%A1%E6%A0%B9%E5%8F%B7%EF%BC%88n%5E2-1%EF%BC%89%2B%E4%B8%89%E6%AC%A1%E6%A0%B9%E5%8F%B7%EF%BC%88n%5E-2n%2B1%EF%BC%89%5D%7D%2C%E5%88%99f%281%29%2Bf%283%29%2Bf%285%29%2B%E2%80%A6%E2%80%A6+%2Bf%28999%29%3D%3F%E5%B7%B2%E7%9F%A5a%E3%80%81b%E3%80%81c%E3%80%81d%E6%98%AF%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E4%B8%94b%2Fa%3D%284d-7%29%2Fc%2C%28b%2B1%29%2F)
1.分解因式:a^4+2a^3b+3a^2b^2+2ab^3+b^42.对於任意自然数n,有f(n)=1/{[三次根号(n^2+2n+10+三次根号(n^2-1)+三次根号(n^-2n+1)]},则f(1)+f(3)+f(5)+…… +f(999)=?已知a、b、c、d是正整数,且b/a=(4d-7)/c,(b+1)/
1.分解因式:a^4+2a^3b+3a^2b^2+2ab^3+b^4
2.对於任意自然数n,有f(n)=
1/{[三次根号(n^2+2n+10+三次根号(n^2-1)+三次根号(n^-2n+1)]},
则f(1)+f(3)+f(5)+…… +f(999)=?
已知a、b、c、d是正整数,且b/a=(4d-7)/c,(b+1)/a=(7b+7)/c,则c/a的值和d/b的值是多少?
1.分解因式:a^4+2a^3b+3a^2b^2+2ab^3+b^42.对於任意自然数n,有f(n)=1/{[三次根号(n^2+2n+10+三次根号(n^2-1)+三次根号(n^-2n+1)]},则f(1)+f(3)+f(5)+…… +f(999)=?已知a、b、c、d是正整数,且b/a=(4d-7)/c,(b+1)/
1.
a^4+2a^3b+3a^2b^2+2ab^3+b^4
=a^4+b^4+2a^2b^2+2a^3b+a^2b^2+2ab^3
=(a^2+b^2)^2+2ab(a^2+b^2)+a^2b^2
=(a^2+ab+b^2)^2
2.对於任意自然数n,有f(n)=
1/{[三次根号(n^2+2n+10+三次根号(n^2-1)+三次根号(n^-2n+1)]},
则f(1)+f(3)+f(5)+…… +f(999)=?
根据a^3-b^3=(a-b)(a^2+ab+b^2)
(n+1)-(n-1)
=[(n+1)^(1/3)]^3-[(n-1)^(1/3)]^3
=[(n+1)^(1/3)-(n-1)^(1/3)]*{(n+1)^(2/3)+(n^2-1)^(1/3)+(n-1)^(2/3)}
=2
f(n)=1/{(n+1)^(2/3)+(n^2-1)^(1/3)+(n-1)^(2/3)}
=[(n+1)^(1/3)-(n-1)^(1/3)]/2
f(1)=1/4^(1/3)=2^(-2/3)
f(1)+f(3)+f(5)+...+f(999)
=f(1)+(1/2)[4^(1/3)-2^(1/3)+6^(1/3)-4^(1/3)+8^(1/3)-6^(1/3)+...+1000^(1/3)-998^(1/3)]
=f(1)+(1/2)[10-2^(1/3)]
=2^(-2/3)-2^(-2/3)+5
=5
已知a、b、c、d是正整数,且b/a=(4d-7)/c,(b+1)/a=(7b+7)/c,则c/a的值和d/b的值是多少?
b/(b+1)=(4d-7)/7(b+1)
7b=4d-7
d=7(b+1)/4
b/a=(4d-7)/c=7b/c
c/a=7