Question

What quantity must be added to each term of the ratio (a+2b) : (a-2b) to make it equal to duplicate ratio of (a+b) : (a-b) ?

=> a:b

=> a²:b

=> b²:a

=> b:a

​

Answer 1

we have to find the quantity that must be added to each term of the ratio (a + 2b) : (a - 2b) to make it equal to duplicate ratio of (a + b) : (a - b).

solution :

concept : x² : y² is the duplicate of x : y.

so, (a + b)² : (a - b)² is the duplicate of (a + b) : (a - b)

let quantity x must be added to the each term of the ratio (a + 2b) : (a - 2b).

⇒{(a + 2b) + x}/{(a - 2b) + x} = (a + b)²/(a - b)²

⇒[{(a + 2b) + x} + {(a - 2b) + x}]/[{(a + 2b) + x} - {(a - 2b) + x}] = [(a + b)² + (a - b)²]/[(a + b)² - (a - b)²]

⇒2(a + x)/4b = 2(a² + b²)/4ab

⇒(a + x)/b = (a² + b²)/ab

⇒(a + x) = (a² + b²)/a

⇒x = (a² + b²)/a - a = (a² + b² - a²)/a

⇒x = b²/a

Therefore the quantity is b² : a