+0  
 
0
39
1
avatar

Find a so that ax^2 + 15x + 4 + 3x + 5 is the square of a binomial.

 Jun 26, 2022
 #1
avatar+124509 
+1

ax^2 + 15x + 4 + 3x + 5          rewrite as

 

ax^2  +18x +  9

 

We need to have

 

( sqrt (a)x + 3)^2 =  ax^2 + 18x + 9

 

a^2  + 2*3sqrt (a) x + 9  =ax^2 + 18x + 9

 

So

 

2*3 sqrt (a)  = 18

 

6 sqrt (a) = 18

 

sqrt (a) =  18 / 6

 

sqrt (a) = 3     square both sides

 

a = 9

 

So  we have

 

( sqrt (9) x + 3)^2  =      (3x + 3)^2  =  9x^2 + 18x + 9

 

 

cool cool cool

 Jun 26, 2022

12 Online Users

avatar
avatar