Question

If 7x – 15y = 4x + y, find the value of x : y. Hence, use componendo and dividend to find the values of:

`(3x^2 + 2y^2)/(3x^2 - 2y^2)`

Answer 1

7x – 15y = 4x + y

7x – 4x = y + 15y

3x = 16y

`x/y = 16/3`

`=> x^2/y^2 = 256/9`

`=> (3x^2)/(2y^2) = (768)/18 = 128/3`  ...`("Multiplying both sides by" 3/2)`

`=> (3x^2 + 2y^2)/(3x^2 - 2y^2) = (128 + 3)/(128 - 3)`   ...(Applying componendo and dividendo)

`=> (3x^2 + 2y^2)/(3x^2 - 2y^2) = 131/125`