Question

If `(a + b)^3/(a - b)^3 = 64/27`

1. Find `(a + b)/(a - b)`
2. Hence using properties of proportion, find a : b.

Answer 1

a. Given `(a + b)^3/(a - b)^3 = 64/27`

Taking cube root on both sides, we get

`(a + b)/(a - b) = root(3)(64/27)`

`implies (a + b)/(a - b) = 4/3`

b. Now `(a + b)/(a - b) = 4/3`

Applying componendo and dividendo, we get

`((a + b) + (a - b))/((a + b) - (a - b)) = (4 + 3)/(4 - 3)`

`\implies (2a)/(2b) = 7/1`

`\implies a/b = 7/1`

Hence, a : b = 7 : 1