Question

One integer is 3 more than another. Their product is 70. How do you find the integers?

Answer 1

`(7,10)` or `(-7,-10)`

Explanation:

Let the integers be `x` and `y` (where let’s say `x > y`)

Conditions given are

• `x = y + 3`

• `xy = 70`

First equation can be written as

`x = 70/x + 3`

`x - 70/x = 3`

`(x^2 - 70)/x = 3`

`x^2 - 70 = 3x`

`x^2 - 3x - 70 = 0`

`x^2 + 10x - 7x - 70 = 0`

`x(x + 10) - 7(x + 10) = 0`

`(x -7)(x + 10) = 0`

`x = -7` or `x = 10`

If `x = -7`

Value of `y` from first equation is

`y = x - 3 = -7 - 3 = -10`

If `x = 10`

Value of `y` from first equation is

`y = x - 3 = 10 - 3 = 7`

Therefore, two sets of integers are possible: `(-7,-10)` and `(7, 10)`