+0  
 
0
81
1
avatar

Given $x\neq0$, find the positive value of $b$ such that the equation 3/x + x/9 = b will have exactly one solution.

 Jun 25, 2022
 #1
avatar+124676 
+1

3/x + x/9   = b      multiply through by x

 

3 + x^2/9  = bx       rearrange  as

 

(1/9)x^2  - bx  + 3  = 0

 

If this has one solution , the  discriminant   =  0 

 

So

 

b^2  - 4(1/9)(3)  = 0

 

b^2  = 12/9

 

b^2  =  4/3     take the positive root

 

b =  2 / sqrt (3)    

 

 

cool cool cool

 Jun 25, 2022

6 Online Users

avatar