Question

63
E) Given that
a + 3ab2
b3 + 3a²b
Using componendo and dividendo, find a : b.
62​

Answer 1

Answer:

a : b = 3 : 2

Step-by-step explanation:

We have

a3 + 3ab2/b3 + 3a2b = 63/62

App.  Componendo and Dividendo

a3 + 3ab2 + b3 + 3a2b/ a3 + 3ab2 - b3 -  3a2b = 63 + 62/63 – 62

a3 + b3 + 3ab2 + 3a2b/a3 + 3ab2 - b3 -  3a2b =  125/1

(a + b)3/(a – b)3 = 125/1

a + b/a – b = 5/1

Again Applying  Componendo and  Dividendo

a + b + a – b/a + b – a + b = 5 + 1/5 – 1

2a/2b = 6/4

a : b = 3 : 2