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Question
If `(a + b)^3/(a - b)^3 = 64/27`.
- Find `(a + b)/(a - b)`
- Hence using properties of proportion, find a : b.
Solution
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
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