Question

The product of two positive numbers is 35 and their difference is 2. What is the sum of the two numbers.

Answer 1

7×5=35
7-5=2
The two numbers are 7 and 5

Answer 2

Answer:

• x  = 7 and y = 5 => their sum: 7+5 = 12

• x = -5 and y =-7 => their sum: -5 + (-7)  = -12

Step-by-step explanation:

Let x is the bigger  number

Let y  is the smaller  number

We have:  

• The product of two positive numbers is 35

=> xy = 35 (1)

• Their difference is 2

=> x - y = 2

<=> x = y+2 (2)

Substitute (2) into (1) we have:

(y+2) y = 35

<=> $y^{2} + 2y - 35 = 0$

<=> y = 5 or y = -7

When y = 5 we get x = 5+ 2 = 7

When y =-7 we get x = -7 +2 = -5  

So we have two possible answers:

• x  = 7 and y = 5 => their sum: 7+5 = 12

• x = -5 and y =-7 => their sum: -5 + (-7)  = -12