Given x/y = 1/4, we can substitute y = 4x into the expression (x^2 - 3xy + y^2) / (x^2 + y^2):
[(x^2 - 3x(4x) + (4x)^2] / (x^2 + (4x)^2)[(x^2 - 12x^2 + 16x^2) / (x^2 + 16x^2)[(5x^2) / (17x^2)5/17
Therefore, the value of (x^2 - 3xy + y^2) / (x^2 + y^2) when x/y = 1/4 is 5/17.
Given x/y = 1/4, we can substitute y = 4x into the expression (x^2 - 3xy + y^2) / (x^2 + y^2):
[(x^2 - 3x(4x) + (4x)^2] / (x^2 + (4x)^2)
[(x^2 - 12x^2 + 16x^2) / (x^2 + 16x^2)
[(5x^2) / (17x^2)
5/17
Therefore, the value of (x^2 - 3xy + y^2) / (x^2 + y^2) when x/y = 1/4 is 5/17.