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41
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Let r and s be the roots of x^2 - 6x - 2 = 0. Find (r - s)^2.

 Jun 25, 2021
 #1
avatar+33551 
+1

(by Vieta's rules)

 

r+s = -6   <======   r^2 +2rs + s^2 = 36       r^2 + s^2 = 36-2rs

 

rs = -2   <====== 

 

 

(r-s)^2 = r^2 -2rs + s^2    

             r^2 + s^2  - 2rs

              36-2rs - 2 rs

               36 -  -4  -  -4    =  44      

 Jun 25, 2021
edited by ElectricPavlov  Jun 25, 2021

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