Expert: Wei Chong - 4/2/2008

Question
what does this question mean and how do i work it out?

A number, x, is equal to its reciprocal plus 1/2

show that 2x(Squared)-x-2=0

thank you

Answer
A number, x, is equal to its reciprocal plus 1/2
.................

This means:

x        -------> Number x

=        -------> is equals to

1/x      -------> its reciprocal

+        -------> plus

1/2      -------> half

So, we have:

x  = 1/x + 1/2

We can continue to show '2x^2-x-2=0' by:    

1) Multiply the equation above by 2x:

 x(2x) = 1(2x)/x + 1(2x)/2

 On the Right Hand Side, we can do some cancellation, we get:

=> 2x^2 = 2 + x     
  
  Now, add both sides with -x, we get:

=> 2x^2 -x = 2        
  
  Finally, add both sides with -2, we get:

=> 2x^2 -x -2 = 0    <-- here is the equation that you need to show.