Question

Write a pair of integers whose difference is 12 and product is -36

Answer 1

Let the integers be x and y.

Therefore,

x - y = 12..........1

xy = -36

or, x = -36/y.......2

Let's substitute value of x from 2 into 1.

x-y = 12

or, -36/y - y = 12

or,( -36-y²)/y = 12

or, -36 - y² = 12y

or , -y² - 12y - 36 = 0

or, -y² -6y - 6y - 36 = 0

or, -y(y+6) -6(y+6)=0

or,( -y-6)(y+6) = 0

Therefore, y must be -6 or 6.

Let's consider y = -6

Then x = -36/y = -36/-6 = 6

Therefore, x = 6

Their difference must be 12

x - y = 6 - (-6) = 6+6 = 12

Hence, x = 6 and y = -6.
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Answer 2

The numbers would be 6 and -6.
Their difference is =6-(-6)
=12
Their product will be= -6*6=-36
To find the answer do prime factorisation of 36 i.e product
36= 2*2*3*3
Make suitable pairs i.e 2*3 & 2*3
Now as we need negative product so one number must be negative