Answer:
x = 3 + √6 ; x = 3 - √6 ;  ;
 ;  
Step-by-step explanation:
Relation given in the question:
 (x² − 6x +3)(2x² − 4x − 7) = 0
Now,
for the above relation to be true the  following condition must be followed:
Either  (x² − 6x +3) = 0 ............(1)
or
(2x² − 4x − 7) = 0 ..........(2)
now considering the equation (1)
(x² − 6x +3) = 0
the roots can be found out as:

for the equation ax² + bx + c = 0
thus,
the roots are

or

or
 and, x =
 and, x = 
or
 and, x =
 and, x = 
or
x = 3 + √6 and x = 3 - √6
similarly for (2x² − 4x − 7) = 0.
we have
the roots are

or

or
 and, x =
 and, x = 
or
 and, x =
 and, x = 
or
 and, x =
 and, x = 
or
 and,
 and, 
Hence, the possible roots are
x = 3 + √6 ; x = 3 - √6 ;  ;
 ; 
 
        
             
        
        
        
4n² - 16n - 84 = 0
Multiply both sides by 1/4 :
n² - 4n - 21 = 0
Add 21 to both sides:
n² - 4n = 21
Complete the square by adding 4 to both sides:
n² - 4n + 4 = 25
(n - 2)² = 25
Solve for n :
n - 2 = ± √25
n - 2 = ± 5
n = 2 ± 5
Then n = 2 + 5 = 7 or n = 2 - 5 = -3.
 
        
             
        
        
        
Answer:

Step-by-step explanation:





 
        
                    
             
        
        
        
Answer:
$182.60
Step-by-step explanation: