化简999...999(2008个9)*999...999(2008个9)+199...999(2008个9)
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化简999...999(2008个9)*999...999(2008个9)+199...999(2008个9)
化简999...999(2008个9)*999...999(2008个9)+199...999(2008个9)
化简999...999(2008个9)*999...999(2008个9)+199...999(2008个9)
100…00(2008个0)的平方
100000(2008个0)^2
999...999(2008个9)*999...999(2008个9)+199...999(2008个9)
=999...999(2008个9)^2+99...999(2008个9)×2+1
=[999...999(2008个9)+1]^2
=1000...000(2008个0)^2
=1000...000(4016个0)
999...999(2008个9)*999...999(2008个9)+199...999(2008个9)
=[100...000(2008个0)-1)*999..99(2008个9)+1999...999(2008个9)
=999..999000..000(2008个9)(2008个0)-999..99(2008个9)+1999...999(2008个9)
=999..999000..000(2008个9)(2008个0)+10000..00(2008个0)
=9999..99(2007个9)8000....000(2008个0)
9*9=81,99*99=9801.999*999=998001
可以确定,最后是1,9过后都是8,8后面的有乘数的数位减1个0.而积中的9也是一样,所以因是999...999(2007个9)8000.00(2007个0)1+199.99(2008个90
后面就不化的太麻烦
(1000……00-1)^2{2008个0}+199...999(2008个9)
=100……00(4016个0)-2x99...999(2008个9)+1++199...999(2008个9)
=100……00(4016个0)-+2
=100……002(4015个0)
设999...999(2008个9)=X
199...999(2008个9)=100...000(2008个0)+999...999(2008个9)
=1+999...999(2008个9)+999...999(2008个9)
原式=X*X+2X+1=(X+1)^2=(10^2008)^2=10^4016
也就是10的4016次方
设999...999(2008个9)=x
则原题是
x^2+x+1000...000(2008个0)
=x(x+1)+1000...000(2008个0)
=1000...000(4016个0)