Question

Write the pair of integer in which multiplication is (-45) and difference is 12​

Answer 1

Appropriate Question:

Write the pair of integer in which multiplication is (-45) and sum is 12.

Required Answer:

The pair of integers can be either (15, -3) or (-3,15).

Explanation:

Given:

• Pair of integers when multiplied gives (-45).
• Pair of integers when added gives 12.

To Find:

• The pair in integers.

Solution:

Let the numbers be x and y.

Here, the equations formed will be:

⇒ x + y = 12

⇒ x × y = (-45)

Solving these equations we will have:

⇒ x + y = 12

⇒ x = 12 - y

⇒ x × y = -45

⇒ (12-y) y = -45

⇒ 12y - y² + 45 = 0

⇒ y² - 15y + 3y - 45 = 0

⇒ y(y-15) + 3(y-15) = 0

⇒ (y - 3) + (y + 3) = 0

So, y = 15 or -3.

Now,

If y = 15 then,

⇒ x = 12 - 15 = (-3)

If y = (-3) then,

⇒ x = 12 - (-3) = 15

So, the pair of integers can be either (15, -3) or (-3,15).