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

Apr 4, 2018

$\left(7 , 10\right)$ or $\left(- 7 , - 10\right)$

#### Explanation:

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

Conditions given are

• $x = y + 3$

• $x y = 70$

First equation can be written as

$x = \frac{70}{x} + 3$

$x - \frac{70}{x} = 3$

$\frac{{x}^{2} - 70}{x} = 3$

${x}^{2} - 70 = 3 x$

${x}^{2} - 3 x - 70 = 0$

${x}^{2} + 10 x - 7 x - 70 = 0$

$x \left(x + 10\right) - 7 \left(x + 10\right) = 0$

$\left(x - 7\right) \left(x + 10\right) = 0$

$x = - 7$ 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: $\left(- 7 , - 10\right)$ and $\left(7 , 10\right)$