Divide 41 into two positive parts such that difference of their squares is 369.
Answers
Answered by
54
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
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
Answered by
35
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