what is the principal of componendo and dividendo & why it is use and how??

Asked by Anshu Chauhan | 9th Sep, 2014, 06:15: AM

Expert Answer:

I f space a over b equals c over d comma space t h e n rightwards double arrow a over b plus 1 equals c over d plus 1 space left square bracket A d d i n g space 1 space o n space b o t h space s i d e s right square bracket rightwards double arrow fraction numerator a plus b over denominator b end fraction equals fraction numerator c plus d over denominator d end fraction space..... left parenthesis i right parenthesis P r i n c i p a l space o f space c o m p o n e n d o I f space a over b equals c over d comma space t h e n rightwards double arrow a over b minus 1 equals c over d minus 1 space left square bracket A d d i n g space 1 space o n space b o t h space s i d e s right square bracket rightwards double arrow fraction numerator a minus b over denominator b end fraction equals fraction numerator c minus d over denominator d end fraction...... left parenthesis i i right parenthesis space P r i n c i p a l space o f space d i v i d e n d o D i v i d i n g space left parenthesis i right parenthesis space b y space left parenthesis i i right parenthesis fraction numerator a plus b over denominator a minus b end fraction equals fraction numerator c plus d over denominator c minus d end fraction space left square bracket C o m p o n e n d o space minus space D i v i d e n d o right square bracket I t space i s space u s e d space i n space p r o p o r t i o n comma space i f space t h e space a p p l i c a t i o n space o f space t h i s space p r o p e r t y space l e a d s space t o space a space s i m p l e r space f o r m space o f space t h e space e q u a t i o n. F o r space E x a m p l e comma I f space fraction numerator x plus y over denominator x minus y end fraction equals 5 over 3 rightwards double arrow fraction numerator x plus y plus x minus y over denominator x plus y minus x plus y end fraction equals fraction numerator 5 plus 3 over denominator 5 minus 3 end fraction left square bracket A p p l y i n g space C o m p o n e n d o minus D i v i d e n d o right square bracket rightwards double arrow fraction numerator 2 x over denominator 2 y end fraction equals 8 over 2 rightwards double arrow x over y equals 4

Answered by Prasenjit Paul | 9th Sep, 2014, 10:04: AM