Question

If a:b= c:d then prove that (a+b+c+d) (a-b-c+d) =(a+b-c-d)(a-b+c-d)

Answer 1

HEY FOLK..

U might get different methods to solve this , I m using a easiest way to solve ,i.e. by applying Compendendo and Dividendendo rule

Your answer is here...

a/b = c/d          (given)
 
If we given with above ratio , by C  and D rule we can say

(a+b)/(a-b) = (c+d)/(c-d)

Cross multiplying...

(a+b)/(c+d) = (a-b)/(c-d)

again by Cand D rule..

[(a+b)+(c+d)] / [(a+b)-(c+d)] = [(a-b)+(c+d)] / [(a-b)-(c-d)]

(a+b+c+d) / (a+b-c-d) = (a-b+c+d) / (a-b-c+d)

Again cross multiplying...

(a+b+c+d)(a-b-c+d) = (a+b-c-d)(a-b+c-d)...........Hence proved

Thank You..

HOPE IT HELPS...! :-)