0 bình luận về “Môn Toán Lớp 8: Giải pt: `{x + 10}/29 + {x – 75}/27 = {x – 73}/25 + {x – 2}/23`”

1. Giải đáp:

    

   Lời giải và giải thích chi tiết:

   $\ \dfrac{x + 10}{29} + \dfrac{x – 75}{27} = \dfrac{x – 73}{25} + \dfrac{x – 2}{23} $

   $\ ⇔ \dfrac{x + 10}{29} – 2 + \dfrac{x – 75}{27} + 1 = \dfrac{x – 73}{25} +1 + \dfrac{x – 2}{23} – 2 $

   $\ ⇔ \dfrac{x + 10 – 58}{29} + \dfrac{x – 75 + 27}{27} = \dfrac{x – 73 + 25}{25} + \dfrac{x – 2 – 46}{23} $

   $\ ⇔ \dfrac{x – 48}{29} + \dfrac{x – 48}{27} = \dfrac{x – 48}{25} + \dfrac{x – 48}{23} $

   $\ ⇔ \dfrac{x – 48}{29} + \dfrac{x – 48}{27} – \dfrac{x – 48}{25} – \dfrac{x – 48}{23} = 0 $

   $\ ⇔ (x – 48)(\dfrac{1}{29} + \dfrac{1}{27} – \dfrac{1}{25} – \dfrac{1}{23}) = 0 $

   Vì $\ \dfrac{1}{29} + \dfrac{1}{27} – \dfrac{1}{25} – \dfrac{1}{23} \neq 0 $

   $\ ⇔ x – 48 = 0 $

   $\ ⇔ x = 48 $

   Vậy phương trình có tập nghiệm $\ S = $ {48}

   Trả lời
2. Giải đáp:

   S = { 48 }

   Lời giải và giải thích chi tiết:

   ( x + 10 )/29 + ( x – 75)/27 = ( x – 73 )/25 + ( x – 2 )/23

   <=> ( ( x + 10 )/29 + ( x – 75)/27 ) – 1 = ( ( x – 73 )/25 + ( x – 2 )/23 ) – 1

   <=> ( ( x + 10 )/29 + ( x – 75)/27 ) – 2 + 1  = ( ( x – 73 )/25 + ( x – 2 )/23 ) – 2 + 1

   <=> ( ( x + 10 )/29 – 2 ) + (  ( x – 75)/27 + 1 ) = ( ( x – 2 )/23 – 2 ) + (  ( x – 73)/25 + 1 )

   <=> ( x + 10 )/29 – 58/29 + ( x – 75)/27 + 27/27 = ( x – 2 )/23 – 46/23 + ( x – 73)/25 + 25/25

   <=> ( x + 10 – 58 )/29 + ( x – 75 + 27 )/27 – ( x – 2 – 46 )/23 – ( x – 73 + 25 )/25 = 0

   <=> ( x – 48 )/29 + ( x – 48 )/27 – ( x – 48 )/23 – ( x – 48 )/25 = 0

   <=> ( x – 48 )( 1/29 + 1/27 – 1/23 – 1/25 ) = 0

   Vì 1/29 + 1/27 – 1/23 – 1/25 != 0

   => x – 48 = 0

   <=> x = 48

   Vậy S = { 48 }

   Trả lời