Question

Find a pair of integers whose product is -36 and whose difference is 15

Answer 1

Hey Mate !

Here is your solution :

Let the numbers are x and y.

According to question ,

=> Product of numbers = -36

=> xy = -36 ----------- ( 1 )

And ,

=> Difference of numbers = 15

=> x - y = 15 ------------ ( 2 )

To find the value of x and y , first we need to find the value of ( x + y ).

Now,

=> ( x + y )² = ( x - y )² + 4xy

By substituting the value of ( 1 ) and ( 2 ),

=> ( x + y )² = ( 15 )² + 4 ( -36 )

=> ( x + y )² = 225 - 144

=> ( x + y )² = 81

=> ( x + y ) = √81

=> ( x + y ) = 9 ---------- ( 3 )

By adding ( 1 ) and ( 3 ) ,

=> x + y + x - y = 9 + 15

=> 2x = 24

=> x = 24 ÷ 2

=> x = 12

By substituting x in ( 1 ),

=> x - y = 15

=> 12 - y = 15

=> -y = 15 - 12

=> -y = 3

=> y = -3

Hence , the numbers are 12 and -3.

==============================

Hope it helps !! ^_^