Question

If a/b _d/c = b/a _ c/d , then prove that a²/b²_ c²/d² = b²/a²_ d²/c² plz explain it , plz ​

Answer 1

Answer:

Given : a/b = c /d

To Find : prove that

(a²+c²) / (b²+d²)=  ca/ db = c²/d²

Solution:

Let  a/b = c/d = k

=> a = bk  and c = dk

  (a²+c²)/  (b²+d² )

= ( (bk)² + (dk)² )/ (b² + d²)

= k²(b² + d²)/(b² + d²)

= k²

ca/db

= dk.bk/db

= dbk²/db

= k²

c²/d²

= (dk)²/d²

= d²k²/d²

= k²

(a²+c²) / (b²+d²)=  ca/ db = c²/d² = k²

Hence Proved

(a²+c²)/(b²+d²)=ca/db=c²/d²