Question

if m and n are root of the equation 1/x-1/x-2=3;where x≠0 and x≠2; find m×n​​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

We have

 

(1/x) - [1/(x-2)] = 3

 

1              1

---   -    ------  =  3

x            x-2

 

The common denominator is x(x-2)

 

1      x-2        1       x

---• -----  -  ----- • ---  = 3

x      x-2       x-2     x

 

 x-2           x

-------  - -------  = 3

x(x-2)     x(x-2)

 

x-2 - x

--------  = 3

x(x-2)

 

-2 = 3x(x-2)

 

-2 = 3x2-6x

 

3x2-6x+2 = 0

 

Using the quadratic formula we can solve for x

 

-b±√(b2-4ac)

--------------

    2a

 

6±√[62-4(3)(2)]

-------------------

    2(3)

 

6±√(36-24)

-------------

      6

 

6±√12

-------

  6

 

6±2√3

-------

   6

 

 

3±√3

------

  3