x² + y² = 36 - 2xy 

=> ( x +y )² = 36 

=> x+y = 6 or -6

x²-y²= 12 

=> (x+y)(x-y) =12 

If x+y = 6 (1)

=> x-y = 2 (2)

(1),(2)=> x=4;y=2 => xy=6

If x+y = -6 (1)

=> x-y = -2 (2)

(1),(2)=> x=-4; y=-2

=> xy = 6

A= (1-\(\dfrac{2}{a}\))(1-\(\dfrac{2}{b}\))(1+\(\dfrac{2}{a}\))(1+\(\dfrac{2}{b}\))

A= ( 1-\(\dfrac{a+b}{a}\))(1-\(\dfrac{a+b}{b}\))(1+\(\dfrac{a+b}{a}\))(1+\(\dfrac{a+b}{b}\))

A= \(\dfrac{b}{a}\).\(\dfrac{a}{b}\).(2+\(\dfrac{b}{a}\))(2+\(\dfrac{a}{b}\))

A= 4 +1 + 2 (\(\dfrac{b}{a}+\dfrac{a}{b}\)) >= 5 +2. 2\(\sqrt{\dfrac{b}{a}.\dfrac{a}{b}}\)= 5+4 =9