Prove that
begin mathsize 20px style open vertical bar table row cell 1 space space end cell cell b c plus a d space space end cell cell b squared c squared plus a squared d squared end cell row cell 1 space end cell cell c a plus b d space space end cell cell c squared a squared plus b squared d squared end cell row cell 1 space end cell cell a b plus c d space space end cell cell a squared b squared plus c squared d squared end cell end table close vertical bar equals open parentheses a minus b close parentheses open parentheses a minus c close parentheses open parentheses a minus d close parentheses open parentheses b minus c close parentheses open parentheses b minus d close parentheses open parentheses c minus d close parentheses end style

Asked by sunil2791 | 22nd Jul, 2017, 09:21: AM

Expert Answer:

begin mathsize 16px style open vertical bar table row 1 cell bc plus ad end cell cell straight b squared straight c squared plus straight a squared straight d squared end cell row 1 cell ca plus bd end cell cell straight c squared straight a squared plus straight b squared straight d squared end cell row 1 cell ab plus cd end cell cell straight a squared straight b squared plus straight c squared straight d squared end cell end table close vertical bar
straight R subscript 1 minus straight R subscript 2 space
open vertical bar table row 0 cell open parentheses straight d minus straight c close parentheses open parentheses straight a minus straight b close parentheses end cell cell open parentheses straight a squared minus straight b squared close parentheses open parentheses straight d squared minus straight c squared close parentheses end cell row 1 cell ca plus bd end cell cell straight c squared straight a squared plus straight b squared straight d squared end cell row 1 cell ab plus cd end cell cell straight a squared straight b squared plus straight c squared straight d squared end cell end table close vertical bar
bc plus ad minus open parentheses ca plus bd close parentheses
equals negative straight c open parentheses straight a minus straight b close parentheses plus straight d open parentheses straight a minus straight b close parentheses
equals open parentheses straight a minus straight b close parentheses open parentheses straight d minus straight c close parentheses
Similarly space straight b squared straight c squared plus straight a squared straight d squared minus open parentheses straight c squared straight a squared plus straight b squared straight d squared close parentheses equals open parentheses straight a squared minus straight b squared close parentheses open parentheses straight d squared minus straight c squared close parentheses
From space the space first space row space we space can space take space open parentheses straight d minus straight c close parentheses open parentheses straight a minus straight b close parentheses space common.
Do space it space for space straight R subscript 2 minus straight R subscript 3 space space you space will space get space common space terms. end style

Answered by Sneha shidid | 24th Jul, 2017, 09:02: AM