Question

If (3x² + 2y²) : (3x² − 2y²) = 11 : 9, find the value of `(3x^4 + 25y^4)/(3x^4 - 25y^4)`.

Answer 1

`(3x^2 + 2y^2)/(3x^2 - 2y^2) = 11/9`

Apply componendo and dividendo

⇒ `((3x^2 + 2y^2) + (3x^2 - 2y^2))/((3x^2 + 2y^2) - (3x^2 - 2y^2)) = (11 + 9)/(11 - 9)`

⇒ `(6x^2)/(4y^2) = 20/2`

⇒ `(3x^2)/(2y^2) = 10`

⇒ `x^2/y^2 = (10 xx 2)/3`

⇒ `x^2/y^2 = 20/3`

`(3x^4/y^4 + 25)/(3x^4/y^4 - 25)`   ...(divided by y⁴)

= `(3(x^2/y^2)^2 + 25)/(3(x^2/y^2)^2 - 25)`

Substitute the value of `x^2/y^2 = 20/3` into the expression:

= `(3(20/3)^2 + 25)/(3(20/3)^2 - 25)`

= `(3(400/9) + 25)/(3(400/9) - 25)`

= `(400/3 + 25)/(400/3 - 25)`

= `((400 + 75)/3)/((400 - 75)/3)`

= `(475/3)/(325/3)`

= `475/325`

= `19/13`