If a : b :: c : d, show that :(i) (a + b)/(c + d) = sqrt( (2a^2 + 7b^2) / (2c^2 + 7d^2) )(ii) (m a^2 + n c^2)/(m b^2 + n d^2) = sqrt( (a^4 + c^4) / (b^4 + d^4) )(iii) (a^2 + ab + b^2)/(a^2 − ab + b^2) = (c^2 + cd + d^2)/(c^2 − cd + d^2)(iv) ((a + c)^3)/((b + d)^3) = a(a − c)^2 / [ b(b − d)^2 ]