+0  
 
0
42
1
avatar

There are two numbers whose sum is 9 times their difference. And the difference of their squares is 81. Find the greater number.

 Feb 9, 2021
 #1
avatar+116125 
+1

a + b  =  9 (a  - b)

a + b =  9a - 9b

-8a  = - 10b

b = 8/10 a   =  4/5 a      (1)

 

And

 

a^2 - b^2   =   81      (sub in (1)  for b )

 

a^2 - [ (4/5)a ] ^2   = 81

 

a^2  - (16/25)a^2  = 81

 

(9/25)a^2  = 81

 

a^2 =  81 * ( 25/9)       take the positive  root

 

a = 9 * (5 / 3 )  =    15

 

b =  (4/5)a =  12

 

 

cool cool cool

 Feb 9, 2021

21 Online Users

avatar
avatar