Ta có : `sin \alpha + cos \alpha  = 5/4`

`<=> ( sin \alpha  + cos \alpha )^2 = (5/4)^2`

`<=> sin^2 \alpha  + 2 sin \alpha  . cos \alpha  + cos^2 \alpha  = 25/16`

`<=> 1 + 2 sin \alpha cos\alpha = 25/16`

`<=> 2 sin \alpha  cos \alpha  = 9/16`

Lại có : `(sin \alpha  - cos \alpha )^2`

`= sin^2 \alpha  - 2 cos \alpha  sin \alpha + cos^2\alpha`

`= 1 - 2 sin \alpha  cos \alpha`

`= 1 - 9/16`

`= 7/16`

Suy ra :  `C = | sin \alpha  - cos \alpha | = | \sqrt{7/16} | = \sqrt{7}/4`

Vậy `C = \sqrt{7}/4`