Question

duplicate ratio of a+c and c+b is a:b prove ab = c2

Answer 1

duplicate proportion of ( a + c) and ( c + b) is a : b
so,
(a + c)²: ( c + b)² = a : b

(a + c)²b = (c + b)²a

a²b + c²b +2acb = c²a + b²a +2bca

a²b - ab²= c²( a -b)

ab( a - b) = c²( a - b)

ab = c²

Answer 2

duplicate proportion of ( a + c) and ( c + b) is a : b

so,

(a + c)²: ( c + b)² = a : b

(a + c)²b = (c + b)²a

a²b + c²b +2acb = c²a + b²a +2bca

a²b - ab²= c²( a -b)

ab( a - b) = c²( a - b)

ab = c²