2道代数奥数题1、已知a是方程x^2-3x+1=0的根,求2a^2-5a-2+3/(a^2+1)的值2、(1/(1+√2))+(1/(√2+√3)))+(1/(√3+√4))+……(1/(√2006+√2007))+(1/(√2007+√2008))=?并且第一个作出两道题的为答案
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![2道代数奥数题1、已知a是方程x^2-3x+1=0的根,求2a^2-5a-2+3/(a^2+1)的值2、(1/(1+√2))+(1/(√2+√3)))+(1/(√3+√4))+……(1/(√2006+√2007))+(1/(√2007+√2008))=?并且第一个作出两道题的为答案](/uploads/image/z/2689657-25-7.jpg?t=2%E9%81%93%E4%BB%A3%E6%95%B0%E5%A5%A5%E6%95%B0%E9%A2%981%E3%80%81%E5%B7%B2%E7%9F%A5a%E6%98%AF%E6%96%B9%E7%A8%8Bx%5E2-3x%2B1%3D0%E7%9A%84%E6%A0%B9%2C%E6%B1%822a%5E2-5a-2%2B3%2F%28a%5E2%2B1%29%E7%9A%84%E5%80%BC2%E3%80%81%281%2F%281%2B%E2%88%9A2%29%29%2B%281%2F%28%E2%88%9A2%2B%E2%88%9A3%29%29%29%2B%281%2F%28%E2%88%9A3%2B%E2%88%9A4%29%29%2B%E2%80%A6%E2%80%A6%281%2F%28%E2%88%9A2006%2B%E2%88%9A2007%29%29%2B%281%2F%28%E2%88%9A2007%2B%E2%88%9A2008%29%29%3D%3F%E5%B9%B6%E4%B8%94%E7%AC%AC%E4%B8%80%E4%B8%AA%E4%BD%9C%E5%87%BA%E4%B8%A4%E9%81%93%E9%A2%98%E7%9A%84%E4%B8%BA%E7%AD%94%E6%A1%88)
2道代数奥数题1、已知a是方程x^2-3x+1=0的根,求2a^2-5a-2+3/(a^2+1)的值2、(1/(1+√2))+(1/(√2+√3)))+(1/(√3+√4))+……(1/(√2006+√2007))+(1/(√2007+√2008))=?并且第一个作出两道题的为答案
2道代数奥数题
1、
已知a是方程x^2-3x+1=0的根,求2a^2-5a-2+3/(a^2+1)的值
2、
(1/(1+√2))+(1/(√2+√3)))+(1/(√3+√4))+……(1/(√2006+√2007))+(1/(√2007+√2008))=?
并且第一个作出两道题的为答案
2道代数奥数题1、已知a是方程x^2-3x+1=0的根,求2a^2-5a-2+3/(a^2+1)的值2、(1/(1+√2))+(1/(√2+√3)))+(1/(√3+√4))+……(1/(√2006+√2007))+(1/(√2007+√2008))=?并且第一个作出两道题的为答案
1.X^2=3X-1则原式=2(3a-1)-5a+3/3a
=6a-2-5a+1/a
=a-2+1/a=(a^2+1)/a-2=3-2=1
2.1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.+1/(√n+√n+1)
=√2-1+√3-√2+√4-√3+...+√(n+1)-√n
=-1+√(n+1)
(1/(1+√2))+(1/(√2+√3)))+(1/(√3+√4))+……(1/(√2006+√2007))+(1/(√2007+√2008))=-1+√2008
1. X^2=3X-1则原式=2(3a-1)-5a+3/3a
=6a-2-5a+1/a
=a-2+1/a=(a^2+1)/a-2=3-2=1
X^2=3X-1则原式=2(3a-1)-5a+3/3a
=6a-2-5a+1/a
=a-2+1/a=(a^2+1)/a-2=3-2=1
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