+0  
 
0
34
1
avatar

The solutions of x(3x-7) = -3  + 2x may be expressed in the form m + sqrt n / p and m - sqrt n / p , where m, n, and p have a greatest common divisor of 1. Find m+n+p.

 Jul 15, 2022
 #1
avatar+124524 
+1

x(3x - 7)  = -3 + 2x

 

3x^2  - 7x  = -3 + 2x           rearrange as

 

3x^2 - 9x  =  -3             divide through by 3

 

x^2  - 3x  =  - 1        complete the square on x

 

x^2  -3x  + 9/4 =  -1  + 9/4

 

(x - 3/2)^2  =  5/4       take  both roots

 

x - 3/2  =     ± √5/2

 

x =   3/2   ± √5/2

 

m= 3    n  = 5     p  =  2

 

m + n +  p  =   10

 

 

 

cool cool cool

 Jul 15, 2022

11 Online Users

avatar
avatar
avatar