+0  
 
0
85
1
avatar

Let x be a positive number such that 2x^2=4x+9-2x+1. If x can be written in simplified form as (a + sqrt(b))/c such that a, b, and c are positive integers, what is a+b+c?

 Jun 29, 2022
 #1
avatar+124676 
+1

Rearrange as

 

2x^2  -2x  =  10   divide through by 2

 

x^2  - 2x   =   5        complete the square on  x

 

x^2 - 2x + 1 =  5 + 1

 

(x - 1)^2 =  6        take the positive root

 

x - 1 =  sqrt (6)

 

x =  1 + sqrt (6)

 

x =  (1 + sqrt (6)  )   / 1

 

a + b + c =      8

 

 

cool cool cool

 Jun 29, 2022

27 Online Users