If A,B are non zero integers and A^8xB^4 - A^4xB 2= 12, which of the following could be A^2 in terms of B?
I. 2/B
II. - 2/B
III. 3/B
:roll: [/spoiler]
I. 2/B
II. - 2/B
III. 3/B
:roll: [/spoiler]
A^8xB^4 - A^4xB^2= 12aditya.j wrote:If A,B are non zero integers and A^8xB^4 - A^4xB 2= 12, which of the following could be A^2 in terms of B?
I. 2/B
II. - 2/B
III. 3/B
:roll:
Option I - A^2 = 2/B =? A^2*B = 2
A^8xB^4 - A^4xB^2 = (A^2*B)^4 - (A^2*B)^2 = 2^4 - 2^2 = 16-4 = 12 Satisfies.
Option II - A^2 = -2/B =? A^2*B = -2
A^8xB^4 - A^4xB^2 = (A^2*B)^4 - (A^2*B)^2 = (-2)^4 - (-2)^2 = 16-4 = 12 Satisfies.
Option III - A^2 = 3/B =? A^2*B = 3
A^8xB^4 - A^4xB^2 = (A^2*B)^4 - (A^2*B)^2 = 3^4 - 3^2 = 27-9 = 18 Nopes!
Option I and II.
You can also solve this solving the equation
A^8xB^4 - A^4xB^2= 12, Let A^4xB^2 = K then
K^2 - K = 12
K(K-1) = 12 where K is an integer
K = 4. i.e. A^4xB^2 = 4,
Implies A^2*B = +2
A^2 = +2/B
