# If X2y2 = 4(xy-1), then prove that X and y very inversely with each other.

We have  :  x2y2 =  4 ( xy - 1 )

$⇒$ x2y2 =  4  xy - 4

$⇒$ x2y2 - 4  xy + 4 = 0

$⇒$ x2y2 + 22  - 2 ( 2 ) (  xy )  = 0

$⇒$ ( x y - 2 ) 2    = 0

$⇒$   x y - 2  = 0

$⇒$   x y  = 2

$⇒$   x   =$\frac{2}{y}$                                ----- ( 1 )

So, From equation 1 we can say x and y very inversely with each other. "                                     ( Prove that )

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