Question

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

Answer 1

Solution is attached below in image

Answer 2

Given:

41 and divided two positive part difference whose square is 369.

To find:

Divide 41 into two positive parts as a whole number

Answer:

Let x = one number part number , which is a one part of 41

Then the other number =(41-x)

$(41-x)^{2}-(x)^{2}=369$

$1681-82x+x^{2}-x^{2}=369$

$-82x = 369 - 1681$

$-82x = -1312$

$x=\frac{-1312}{-82}$

x = +16 is one number

Therefore, the other positive part number is,

$41\quad -\quad 16\quad =\quad 25$

Verification:

$25^2\quad -\quad 16^2\quad$

$=\quad 625\quad -\quad 256$

$25^2\quad -\quad 16^2\quad =\quad 369$