`{( 2x + y = 5m - 1 ),( x - 2y = 2 ):}`

`{( 4x + 2y = 10m - 2 ),( x - 2y = 2 ):}`

`{( 5x = 10m ),( x = 2y + 2 ):}`

`{( x = 2m ),( 2m = 2y + 2 ):}`

`{( x = 2m ),( y = m - 1 ):}`

Lại có: `x^2 - 2y^2 = 1`

`4m^2 - 2( m^2 - 2m + 1 ) = 1`

`4m^2 - 2m^2 + 4m - 2 = 1`

`2m^2 + 4m + 2 = 5`

`2( m + 1 )^2 = 5`

`( m + 1 )^2 = 5/2`

`m = ( -2 +-\sqrt{10})/2`

`Vậy  m in { ( -2 +- \sqrt{10} )/2 }`