(i) 21x^² + 10x + 1 = 0

(ii) 24y^²+ 26y + 5 = 0

$21{x^2} + 10x + 1 = 0$

$21{x^2} + 7x + 3x + 1 = 0$

$7xleft( {3x + 1} ight) + 1left( {3x + 1} ight) = 0$

$x = frac{{ - 1}}{3},frac{{ - 1}}{7}$

$24{y^2} + 26y + 5 = 0$

$24{y^2} + left( {20 + 6} ight)y + 5 = 0$

$24{y^2} + 20y + 6y + 5 = 0$

$4yleft( {6y + 5} ight) + 1left( {6y + 5} ight) = 0$

$y = frac{{ - 5}}{6}, - frac{1}{4}$

No relation between x and y