# The sum of two numbers is 25, the sum of their squares is 313. What are the numbers?

##### 3 Answers

#### Explanation:

If

Substitute:

#### Explanation:

Suppose the two numbers are

"The sum of two numbers is 25" gives us:

# a+b=25 #

"sum of their squares is 313" gives us:

# a^2+b^2=313 #

From the first equation we have:

# b=25-a#

Substituting for

# a^2+(25-a)^2=313 #

# :. a^2+625-50a+a^2=313 #

# :. 2a^2-50a+312=0 #

# :. a^2-25a+156=0 #

# :. (a-12)(a-13)=0 #

# :. a=12,13 #

We now use the second equation to find the value of

# a=12 => b=25 - 12 = 13 #

# a=13 => b=25 - 13 = 12 #

So there is only one solution which is that the two numbers are

The numbers are

#### Explanation:

Let te numbers be

therefore we have **............(1)**

which gives us **............(2)**

and we also have **............(3)**

Subtracting (3) from (2), we get **............(4)**

and (4) from (3) we get

**............(5)**

i.e. **............(6)**

Slolving for

Note:we can also have