Question

the difference between two numbers is 2 and their product is 1443 find the numbers

Answer 1

Define x:

Let one number be x

The other number is x - 2

Solve x:

x(x - 2) = 1443

x² - 2x - 1443 = 0

(x - 39)( x + 37) = 0

x = 39 or x = -37

Find the numbers:

One numer = x = 39

The other number = x - 2 = 39 - 2 = 37

OR

one number = x = -37

The other number = x - 2 = -37 - 2 = -39

Answer: The numbers are 37 and 39 or -37 and -39

Answer 2

Given:

• Difference between two numbers is 2
• Product is 1443

Assumptions:

Let a and b be two numbers.

Consider x representing the numbers.

Solution:

By condition,

x(x - 2) = 1443

x² - 2x - 1443 = 0

By solving,

We get two factors,

(x - 39)( x + 37) = 0

x = 39 or x = -37

If a = 39,

Then,

b = 37

Proof:

39*37 = 1443

39-37 = 2

Hence, a = 39 and b = 37

If a = -37,

Then,

b = -39

Proof:

-37*-39 = 1443

-37-(-39) = 2

Hence, a = -37 and b = -39