`c,` Ta có `: ( 2x - 5 )^2018 ≥ 0 ; ( 3y + 4 )^2020 ≥ 0`

`⇒ ( 2x - 5 )^2018 + ( 3y + 4 )^2020 ≥ 0`

Theo đề bài `,` ta có `:`

`( 2x - 5 )^2018 + ( 3y + 4 )^2020`

`⇒ ( 2x - 5 )^2018 = 0`

    `( 3y + 4 )^2020 = 0`

`⇔ 2x - 5 = 0`

     `3y + 4 = 0`

`⇔ 2x = 5`

    `3y = 4`

`⇔ x = 5/2` 

     `y = 4/3`

Lại có `: M + ( 5x^2 - 2xy ) = 6x^2 + 9xy - y^2`

`⇔ M + 5x^3 - 2xy = 6x^2 + 9xy - y^2`

`⇔ M = 6x^2 + 9xy - y^2 - 5x^3 + 2xy`

`⇔ M = x^2 + 11xy - y^2`

Thay `x = 5/2 , y = ( - 4 )/3` vào `,` ta được `:`

`M = ( 5/2 )^2 + 11 . 5/2 . ( - 4 )/3 - ( ( - 4 )/3 )^2`

`M = 25/4 + 55/2 . ( - 4 )/3 - 16/9`

`M = 25/4 + ( - 110 )/3 - 16/9`

`M = ( - 1159 )/36`

Vậy `, M = ( - 1159 )/36 .`

Bài `2 :`

`a, ( - 15 )/12 x + 3/7 = 6/5 x - 1/2`

`⇔ ( - 5 )/4 x + 3/7 - ( 6/5 x - 1/2 ) = 0`

`⇔ ( - 5 )/4 x + 3/7 - 6/5 x + 1/2 = 0`

`⇔ x . ( ( - 5 )/4 - 6/5 ) + ( 3/7 + 1/2 ) = 0`

`⇔ x . ( - 49 )/20 + 13/14 = 0`

`⇔ x . ( - 49 )/20 = 0 - 13/14`

`⇔ x . ( - 49 )/20 = ( - 13 )/14`

`⇔ x = ( - 13 )/14 : ( - 49 )/20`

`⇔ x = 130/343`

Vậy `, x = 130/343 .`

`b, 1/( 3 . 5 ) + 1/( 5 . 7 ) + ..... + 1/( ( 2x - 1 ) . ( 2x + 1 ) ) = 49/99`

`⇔ 1/2 . ( 2/( 1 . 3 )  + 2/( 3 . 5 ) + .... + 2/( ( 2x - 1 ) . ( 2x + 1 ) ) = 49/99`

`⇔ 1/1 - 1/3 + 1/3 - 1/5 + .... + 1/( 2x - 1 ) - 1/( 2x + 1 ) = 49/99 : 1/2`

`⇔ 1 - 1/( 2x + 1 ) = 98/99`

`⇔ 1/( 2x + 1 ) = 1 - 98/99`

`⇔ 1/( 2x + 1 ) = 1/99`

`⇔ 2x + 1 = 99`

`⇔ 2x = 99 - 1`

`⇔ 2x = 98`

`⇔ x = 98 : 2`

`⇔ x = 49`

Vậy `, x = 49 .` 

`c, 2xy - x - y = 2`

`⇔ 2 . ( 2xy - x - y ) = 2 . 2`

`⇔ 2 . 2xy - 2x - 2y = 4`

`⇔ 2x . ( 2y - 1 ) - 2y + 1 - 1 = 4`

`⇔ 2x . ( 2y - 1 ) - ( 2y - 1 ) = 4 + 1`

`⇔ ( 2x - 1 ) . ( 2y - 1 ) = 5`

Mà `x , y ∈ Z ⇒ ( 2y - 1 ) . ( 2x - 1 ) = 1 . 5 = ( - 1 ) . ( - 5 )` 

Ta có bảng sau `:`      

\begin{array}{|c|c|c|}\hline \text{2x - 1}&\text{5}&\text{1}&\text{- 1}&\text{- 5}\\\hline \text{2y - 1}&\text{1}&\text{5}&\text{- 5}&\text{- 1}\\\hline \text{x}&\text{3}&\text{1}&\text{0}&\text{- 2}\\\hline \text{y}&\text{1}&\text{3}&\text{- 2}&\text{0}\\\hline\end{array}

Vậy `, { x ; y } ∈ { ( 3 ;  1 ) , ( 1 ; 3 ) , ( 0 ; - 2 ) , ( - 2 ; 0 ) } .`

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