Question

求方程x/1*3+x/3*5+x/5*7+.+x/1993*1997=997

Answer 1

x/1*3+x/3*5+x/5*7+.+x/1993*1997=997

(1/1*3+1/3*5+1/5*7+.+1/1993*1997)x=997

[1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+……+1/2(1/1995-1/1997)]x=997

1/2x(1-1/3+1/3-1/5+1/5-1/7+……+1/1995-1/1997)=997

1/2x*1996/1997=997

1996/3994x=997

x=997*3994/1996

x=3982018/1996

x=1994+1994/1996

x=1994+997/998

x=1994又997/998