+0  
 
0
9
1
avatar+1679 

Let $r$ and $s$ be the roots of $2x^2 + 5x - 13 = x^2 - 4x + 7.$  Find $r^2 + s^2.$

 Dec 18, 2023
 #1
avatar+129431 
+1

Simplify as

 

x^2  + 9x - 20   =    0

 

r + s =   -9/1 =  -9        square both sides

r^2 + 2rs + s^2  =   81         (1)

 

rs =   -20 / 1  =  -20

2rs  =  -40

 

So......using (1)

 

r^2  + 2 (-40) + s^2   =  81

 

r^2  - 80 + s^2  =  81

 

r^2 + s^2  =   81 + 80

 

r^2 + s^2  =  161

 

 

cool cool cool

 Dec 19, 2023

7 Online Users

avatar
avatar
avatar
avatar