Giải phương trình sau: $\frac{x-5}{1990}$ + $\frac{x-15}{1980}$ + $\frac{x-25}{1970}$ = $\frac{x-1990}{5}$ + $\frac{x-1980}{15}$ + $\frac{x-1970}{25}

0 bình luận về “Giải phương trình sau: $\frac{x-5}{1990}$ + $\frac{x-15}{1980}$ + $\frac{x-25}{1970}$ = $\frac{x-1990}{5}$ + $\frac{x-1980}{15}$ + $\frac{x-1970}{25}”

1. x-5/1990 + x-15/1980 + x-25/1970 = x-1990/5 + x-1980/15 + x-1970/25

   ⇔ ( x-5/1990 – 1 ) + ( x-15/1980 -1 ) + ( x-25/1970 -1 ) = ( x-1990/5 -1 ) + ( x-1980/15 -1 ) + ( x-1970/25 -1 )

   ⇔ x-1995/1990 + x-1995/1980 + x-1995/1970 = x-1995/5 + x-1995/15 + x-1995/25

   ⇔ ( x-1995 )(1/1990+1/1980+1/1970-1/5-1/15-1/25) = 0

   ⇔ x-1995 = 0

   ⇔ x = 0+ 1995

   ⇔ x = 1995

    

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