Two numbers add up to 2 and their difference is 4. What is their product?

Question

I have been trying this for quite some time but I can't seem to get the numbers right 

Answer 1

Let the one number = x

Let the other number = y

 

 

Set equations that shows sum and difference.

 

x + y = 2                  eq1

x - y = 4                    eq2

 

 

We have a system of equations.

 

 

Subtract eq2 from eq1 to eliminate the x terms.

 

2y = -2

 

 y = -1

 

 

Substitute this value of y into eq1 to solve for x.

 

x = 2 - y

x = 2 - (-1)

x = 3

 

 

The numbers are -1 and 3.  

 

 

Multiply these numbers and you will have your answer.

 

Answer 2

Let the two numbers are a and b.

 

Given,

  sum of two numbers i.e.  a+b  = 2

  difference of these numbers (this one is tricky)    either    a-b = 4  

                                                                                             or    b-a = 4

  now we use the relation,

 

             (a+b)² = (a-b)² + 4 ab  

                 2²   =    4²    + 4 ab     , as we know that (a-b)²=(b-a)² =4²

                 4     =   16     + 4 ab

                4-16  =   4 ab

                - 12   =  4 ab

               -12/4   = ab

                -3     = ab

 

 

 

So we have the product of the numbers a and b = ab

                                                                      = -3

Answer 3

Chong,

 

This can be fairly "tricky" at first glance. Let's setup a few equations.

 

We will assign a and b for the two numbers. 

 

The two numbers add up to 2, we write like:

 

a + b = 2 

 

Since we don't know which of these numbers is the largest, we must assume the absolute value of |b-a| = 4 

 

Thus, from the absolute value, we get: 

 

b - a = 4 

and, b - a = -4 

 

take the second equation and solve it for b. 

 

We get: b = -4 + a 

 

Plug this equation into the sum equation that we generated first, and we get: 

 

a + (-4 + a) = 2. Solve: 

 

2a + (-4) = 2 

 

Thus, a = 3 

b = -1 

 

Let's check our answers: 

 

3 + (-1) = 2 

 

(-1) - 3 = -4 

 

Although the problem did not explicitly outline the positive difference, we must consider the negative value as well because the difference between these two numbers on the number line is indeed 4, we don't care about the direction just the units.

 

Thus, the product would be a negative (-) 3.

 

Hope this helps!