数学简便计算

Question

1 99......9*99......9+199.....9= 注：每个都是88个9
2 （1999*99+2000*100+1999+2000——1900）/4000=
写出计算过程

Answer 1

设x=99.999 (88个9)

99......9*99......9+199.....9
=x*x+(x+1)+x
=x*x+2x+1
=(x+1)(x+1)
=100..00 (176个0)

(1999*99+2000*100+1999+2000-1900）/4000
=(1999*99+1999+2000*100+100）/4000
=(1999*100+100+2000*100)/4000
=2000*100*2/4000
=100

Answer 2

85*125-3*125-2*125

Answer 3

99......9*99......9+199.....9
=(10^88-1)^2+10^88+10^88-1---------因为199.....9=10^88+9.....9
=10^176-2*10^88+1+10^88+10^88-1
=10^176

（1999*99+2000*100+1999+2000——1900）/4000
=[(999*99+1999)+2000*100+(2000—1900）]/4000
=[1999*100+2000*100+100]/4000
=(1999+2000+1)*100/4000
=4000*100/4000
=100