Question

Divide 41 into two positive parts such that the differnce of their square is 369. Form an eqiation.

Answer 1

Let  first number = x

and second number = 41-x

( 41 - x )² -  (x)²  =  369

By using identity ( a - b )² below

(41)² + (x)² - 2 × 41 × x    -   x²   = 369

1681 + x² - 82x - x² = 369

Above, one x square is positive and one x square is negative. so, they will cancel each other.

1681 - 82x  = 369

- 82x = 369 - 1681

- 82x  =  - 1312

       x  =   - 1312/ - 82
        
      x  = 16

So, 
      First number is x =  16

and Second number is 41-x  =   41 - 16
                                             
                                              = 25
  

you can also check the answer.

= (25)² - (16)² 

= 625 - 256

= 369

I HOPE THIS HELP U :-)
 
BEST OF LUCK FOR YOUR EXAM




 

Answer 2

Let  first number = x
and second number = 41-x
( 41 - x )² -  (x)²  =  369
By using identity ( a - b )² below
(41)² + (x)² - 2 × 41 × x    -   x²   = 369
1681 + x² - 82x - x² = 369
1681 - 82x  = 369
- 82x = 369 - 1681
- 82x  =  - 1312
       x  =   - 1312/ - 82 
      x  = 16

First number is x =  16
and Second number is 41-x  =   41 - 16
                                              
                                              = 25