Question

If (11a^2+ 13b^2) (11c^2- 13d^2) = (11 a^2 - 13b^2) (11c^2 + 13d^2), prove that a: b : : c : d.​

Answer 1

$\fontsize{18}{10}{\textup{\textbf{Hence proved a:b::c:d}}}$

Step-by-step explanation:

Given equation

(11a^2+ 13b^2) (11c^2- 13d^2) = (11 a^2 - 13b^2) (11c^2 + 13d^2)

=>(11a^2+ 13b^2) /(11 a^2 - 13b^2) =(11 a^2 - 13b^2)/ (11c^2- 13d^2)

By componendo and dividendo

=>{(11a^2+ 13b^2)+(11 a^2 - 13b^2)} /{(11 a^2 + 13b^2)-(11 a^2 - 13b^2)}={(11 a^2 - 13b^2)+(11c^2- 13d^2)}/ {(11c^2+ 13d^2)-(11c^2- 13d^2)}

=>22a^2/26b^2=22c^2/26d^2

=>a/c=c/d

Hence

a:b::c:d