1.x=√3-2,求x4+4x3-3x2-16x-4的值.2.设S=√(1+1/1^2+1/2^2)+√(1+1/2^2+1/3^2)+√(1+1/3^2+1/4^2)+……+√(1+1/2009^2+1/2010^2),则与S最接近的整数是多少?
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![1.x=√3-2,求x4+4x3-3x2-16x-4的值.2.设S=√(1+1/1^2+1/2^2)+√(1+1/2^2+1/3^2)+√(1+1/3^2+1/4^2)+……+√(1+1/2009^2+1/2010^2),则与S最接近的整数是多少?](/uploads/image/z/11460789-45-9.jpg?t=1.x%3D%E2%88%9A3-2%2C%E6%B1%82x4%2B4x3-3x2-16x-4%E7%9A%84%E5%80%BC.2.%E8%AE%BES%3D%E2%88%9A%281%2B1%2F1%5E2%2B1%2F2%5E2%29%2B%E2%88%9A%EF%BC%881%2B1%2F2%5E2%2B1%2F3%5E2%29%2B%E2%88%9A%EF%BC%881%2B1%2F3%5E2%2B1%2F4%5E2%29%2B%E2%80%A6%E2%80%A6%2B%E2%88%9A%281%2B1%2F2009%5E2%2B1%2F2010%5E2%29%2C%E5%88%99%E4%B8%8ES%E6%9C%80%E6%8E%A5%E8%BF%91%E7%9A%84%E6%95%B4%E6%95%B0%E6%98%AF%E5%A4%9A%E5%B0%91%3F)
1.x=√3-2,求x4+4x3-3x2-16x-4的值.2.设S=√(1+1/1^2+1/2^2)+√(1+1/2^2+1/3^2)+√(1+1/3^2+1/4^2)+……+√(1+1/2009^2+1/2010^2),则与S最接近的整数是多少?
1.x=√3-2,求x4+4x3-3x2-16x-4的值.
2.设S=√(1+1/1^2+1/2^2)+√(1+1/2^2+1/3^2)+√(1+1/3^2+1/4^2)+……+√(1+1/2009^2+1/2010^2),则与S最接近的整数是多少?
1.x=√3-2,求x4+4x3-3x2-16x-4的值.2.设S=√(1+1/1^2+1/2^2)+√(1+1/2^2+1/3^2)+√(1+1/3^2+1/4^2)+……+√(1+1/2009^2+1/2010^2),则与S最接近的整数是多少?
1、x^4+4x^3-3x^2-16x-4=x^4+4x^3+4x^2-7x^2-16x-4=(x^4+4x^3+4x^2)-(7x^2+16x+4)=x^2(x+2)^2-(x+2)(7x+2)
将x==√3-2代入,得:
原式=3(7-4√3)-√3(7√3-12)=21-12√3-21+12√3=0
2、此题应先找出各项的通式,并化简.
√1+1/a^2+1/(a+1)^2
=√[a^2+(a+1)^2+a^2·(a+1)^2]/a^2·(a+1)^2
=√a^4+2a^3+3a^2+2a+1/[a(a+1)]^2
=√a^2·(a+1)^2+2a(a+1)+1/[a(a+1)]^2
=√(a^2+a+1)^2/[a(a+1)]^2
=(a^2+a+1)/a(a+1)
=1+1/a(a+1)
=1+1/a-1/(a+1)
所以,原式可化为
(1+1/1-1/2)+(1+1/2-1/3)+(1+1/3-1/4)+……+(1+1/2009-1/2010)
=2009+(1/1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010)
=2009+1-1/2010
=2010-1/2010