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`6x^2 + 5y^2 = 74`

`<=> 6x^2 - 24 =50 - 5y^2`

`<=> 6(x^2 - 4) = 5(10 - y^2)`

Ta có:

`x^2 - 4 >= -4 AA x`

`10 - y^2 <= 10 AA y`

`=> 6(x^2 - 4) >= -24; 5(10 - y^2) <= 50 AA x,y`

`=> -24 <= 6(x^2 - 4) <= 50`

`=> 6(x^2 - 4) in {-24 ;-18 ; -12; -6; 0; 6; 12; 18; 24; 30; 36; 42; 48}`

`=> x^2 in {0 ; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12}`

Vì `x in ZZ` nên ta có:

`{(x = 0 => y^2 = 74/5(l) ),(x = +-1 => y^2 = 68/5(l)),(x = +-2 => y^2 = 10(l)),(x = +-3 => y^2 = 4(tm) => y in {2; -2}):}`

Vậy `(x; y) = (3; 2);(3 ; -2);(-3;2);(-3;-2).`