Question

Divide 41 into two parts such that the difference of their squares is 369

Answer 1

Here is your answer

Let x = one number
then
(41-x) = the other number
:
(41-x)^2 - x^2 = 369
FOIL
1681 - 82x + x^2 - x^2 = 369
-82x = 369 - 1681
-82x = -1312
x = -1312/-82
x = +16 is one number
and
41 - 16 = 25 is the other number
:
:
Check
25^2 - 16^2 =
625 - 256 = 369 

HOPE IT HELPS YOU

Answer 2

let the parts be 'x' and 'y'
ATQ
x + y = 41. eq.1
x^2 - y^2 = 369. eq.2

Eq.2
x^2 - y^2 = 369
(x+y) (x-y) = 369
(41) (x-y) = 369
41x - 41y = 369
x - y = 9. eq.3
(Dividing the whole equation by 41 )

Adding eq.1 and eq.3 we get
2x = 50
x = 25
Putting this value in eq.3
25 - y = 9
y = 16
So the two parts are 25 and 16 .