SOLUTION: Divide 41 into two positive parts such that difference of their squares is 369.

Question 696756:

Divide 41 into two positive parts such that difference of their squares is 369.
Found 2 solutions by ankor@dixie-net.com, checkley79:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Divide 41 into two positive parts such that difference of their squares is 369
:
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
Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
LET X & (41-X) BE THE 2 POSITIVE PARTS.
X^2-(41-X)^2=369
X^2-1681+82X-X^2=369
82X=369+1681
82X=2050
X=2050/82
X=25 ANS. FOR THE LARGER PART.
41-25=16 ANS. FOR THE SMALLER PART.
PROOF:
25^2-16^2=369
625-256=369
369=369

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