+0  
 
0
109
1
avatar

Find 1/(a - 1) + 1/(b - 1), where a and b are the roots of the quadratic equation 2x^2 - 9x + 2 = 0.

 Jun 15, 2021
 #1
avatar+121063 
+2

By Vieta

 

The  sum of the  roots  =  a + b =  9/2

The product of the  roots =  ab  =  2/2  =  1

 

And note that

 

1/ ( a - 1)    +  1  /( b - 1)   =   

 

b -1   +  a  - 1

_____________   =

(a - 1)  ( b - 1)

 

   a + b  - 2

____________  =

ab  - a - b  + 1

 

 

( a + b)  - 2

_______________    =

ab  - (a + b) + 1

 

   9/2   - 2

__________   =

1 - (9/2) + 1

 

     5/2

_______   =

    -5/2

 

-1

 

 

cool cool cool

 Jun 15, 2021

38 Online Users

avatar
avatar