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
which gives us
and we also have
Subtracting (3) from (2), we get
and (4) from (3) we get
i.e.
Slolving for
Note:we can also have