Write a pair of integers whose product is – 36 and whose difference is 15.

Let the integers be x and y, where x > y.

According to the question,

Product of integers = -36

⇒ x × y = -36

⇒ xy = -36 …(i)

Also, difference of integers = 15

⇒ x – y = 15 …(ii)

From equation (i),

xy = -36

⇒ …(iii)

Substituting equation (iii) into equation (ii), we get

⇒

⇒ x² + 36 = 15x

⇒ x² – 15x + 36 = 0

⇒ x² – 12x – 3x + 36 = 0

⇒ x(x – 12) – 3(x – 12) = 0

⇒ (x – 3)(x – 12) = 0

⇒ x = 3 or x = 12

If x = 3,

Put x = 3 in equation (ii),

x – y = 15

⇒ 3 – y = 15

⇒ y = 3 – 15

⇒ y = -12

One of the pair is (3, -12).

If x = 12,

Put x = 12 in equation (i),

x – y = 15

⇒ 12 – y = 15

⇒ y = 12 – 15

⇒ y = -3

One of the pair is (12, -3).

Thus, two solutions are (3, -12) and (12, -3).