If (x+y): (x-y)=7: 3, then find the ratio of (x^2+ y^2): (x^2-y^2).

(x+y):(x-y) = 7:3

1) $(x+y)*(x-y) = 21k^2$

$x^2 - y^2 = 21k^2$ ......a

2) $(x+y)*(x+y) = 49 k^2$

$x^2 + y^2 + 2xy = 49 k^2$ .......b

3) $(x-y)*(x-y) = 9 k^2$

$x^2 + y^2 - 2xy = 9 k^2$ ...c

Equation b + c,

$2(x^2 + y^2) = 58 k^2$

$(x^2 + y^2) = 29 k^2$

$(x^2+ y^2): (x^2-y^2)$ = 29:21

The correct answer is Option (2) → 29 : 21