SOLUTION: separate 65 into two parts so that the square of the smaller is 455 less than the square of the larger. what is the answer?

Question 339068: separate 65 into two parts so that the square of the smaller is 455 less than the square of the larger. what is the answer?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
separate 65 into two parts so that the square of the smaller is 455 less than the square of the larger. what is the answer?
:
Let x = one part
then
(65-x) = the other part (the larger part)
:
The statement essentially says:
(65-x)^2 - x^2 = 455
;
FOIL (65-x)(65-x)
4225 - 130x + x^2 - x^2 = 455
-130x = 455 - 4225
-130x = -3770
x =
x = +29 is the smaller
and
65 - 29 = 36 is the larger part
:
:
:
See if that's true
36^2 - 29^2 =
1296 - 841 = 455; confirms our solution
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