If (x³ – y³) : (x² + xy + y²) = 5 : 1 and (x² – y²) : (x – y ) = 7 : 1, then fing the value of x : y-  

6 : 1

(x³ – y³) : (x² + xy + y²) = 5 : 1

Using identity, (x³ – y³)= (x - y) (x² + xy + y²)

(x - y) : 1 = 5 : 1

Thus, (x - y) = 5     ______ (i)

Also, (x² – y²) : (x – y ) = 7 : 1

Using identity,  (x² – y²) = (x -y)(x + y)

 (x + y) : 1 = 7 : 1

Thus, (x + y) = 7     _______(ii)

Solving eq, (i) and (ii)

2x = 12 or x = 6

and y = 1

x : y = 6 : 1