Factorization -- formula of square difference 4X & sup2; - Y & sup2; = 12x, y are positive integers. Find the value of X, y

Factorization -- formula of square difference 4X & sup2; - Y & sup2; = 12x, y are positive integers. Find the value of X, y

Factoring the left
(2x+y)(2x-y)=12
Because X and y are positive integers
So 2x + Y > 2x-y
(2x + y) - (2x-y) = 2Y is even
So 2x + y = 6
And 2x-y = 2
The solution is x = 2, y = 2

Using square difference formula to decompose two factors
（1）4x^2-(-y)^2
（2）-4x^2-y^2

（1）4x^2-(-y)^2=（2x）^2-y^2=(2x+2)(2x-2)
（2）-4x^2+y^2=-[(2x)^2-y^2]=-(2x+2)(2x-2)
The second is definitely wrong! The second minus should be a plus sign, or the first - yes+

If the negative first power of 1-4x + the negative second power of 4x = 0, then the negative second power of x2-x is?

1-4x^-1+4x^-2=0
Multiply X & sup2 on both sides;
x²-4x+4=0
(x-2)²=0
x=2
Original formula = 4-1 / 4 = 15 / 4