Question

If a : b = 9 : 10, find the value of `(2a^2 - 3b^2)/(2a^2 + 3b^2)`

Answer 1

a : b = 9 : 10
⇒ `a/b = (9)/(10)`

`(2a^2 - 3b^2)/(2a^2 + 3b^2)`

= `((2a^2)/(b^2) - (3b^2)/(b^2))/((2a^2)/(b^2) - (3b^2)/(b^2))`  ...(Dividing by b²)

= `(2(a/b)^2 - 3)/(2(a/b)^2 + 3`

= `(2(9/10)^2 - 3)/(2(9/10)^2 + 3)`

= `(2 xx 81/100 - 3)/(2 xx 81/100 + 3)`

= `(81/50 - 3)/(81/50 + 3)`

= `((81 - 150)/(50))/((81 + 150)/(50)`

= `(-69)/(50) xx (50)/(231)`

= `(-69)/(231)`

= `-(23)/(77)`