The equivalent resistance of a series combination of two resistors is '9 Omega' and the equivalent resistance of a parallel combination of the same two resistors is `2 Omega`. Find the resistances of the resistors.

Explanation

Suppose two unknown resistances are x and y.
When the resistors are connected in parallel `(xy)/(x +y) = 2Omega` and when they are connected in series `x +y = 9 Omega`
So, `(xy)/9 = 2 :. Xy = 18 Omega`
Now,
From `x +y = 9 , y = 9-x`
`:. x (9-x) =18`
`:. 9 x -x^2 =18`
`:. x^2 -9x + 18 = 0`
`:. x- 6x - 3x + 18 =0`
`:. x(x-6)-3 (x-6)=0`
`:.(x -3) (x -6) =0`
`:. x =3 Omega or x = 6Omega`
Hence `y = 9-x =9-3 = 6 Omega or y =9 -6 = 3Omega`
Thus, ` x=3 Omega and y = 6Omega or x =6 Omega and y = 3Omega`