Question

if x square y square= 4(xy-1),then prove that x and y vary inversely as each other. ( Hint : prove xy = constant.

Answer 1

hey mate
here's the solution

Answer 2

X and Y vary inversely as each other.

Step-by-step explanation:

1. Here given that

  $X^{2}Y^{2}= 4(XY-1)$    ...1)

2. Equation 1) can be written as

  $X^{2}Y^{2}= 4XY-4$

  So

 $X^{2}Y^{2}-4XY+4=0$   ...2)

3. By comparing the identity  $A^{2}-2AB+B^{2}=(A-B)^{2}$ to left side of equation 2)

4. We get

   A= XY and B =2

5. So equation 2) can be written as

    $X^{2}Y^{2}-4XY+4=0$  

    Means

    $(XY-2)^{2}=0$      

   So

  XY-2=0          ...3)

6.  From equation 3)

    $Y=\frac{2}{X}$      ...4)

    Or

    $X=\frac{2}{Y}$      ...5)

7. From equation 4 and equation 5) it is clear that X and Y are vary inversely.