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?
:
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 = {{{(-3770)/(-130)}}}
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