+0  
 
0
26
1
avatar+1827 

Fill in the blanks with positive integers:

(3 + sqrt(5) - 1 + 2*sqrt(3) + 5)^2 = ___ + ___ *sqrt(5)

 Dec 14, 2023
 #1
avatar+129245 
+1

Simplify  as

(7 + sqrt 5 + 2sqrt 3)^2 =    (7 + sqrt (5) + sqrt (12))^2

 

[ (7 + sqrt 5) + sqrt (12) ]  [ (7 + sqrt (5) + sqrt (12) ] =

 

(7 + sqrt 5)^2 + 2 [ (7 + sqrt (5)) * sqrt (12) ]  +  (sqrt (12))^2  =

 

49 + 14 sqrt 5 + 5  + 2*7 sqrt (12) + 2sqrt (60) + 12  =

 

66 + 14sqrt (5) + 14 sqrt (12) + 4sqrt (15)  =

 

66 + 14sqrt (5) + 28sqrt (3) + 4sqrt(15)

 

 

cool cool cool

 Dec 14, 2023

3 Online Users

avatar