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

Question

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

juanma92goz · Accepted Answer

If       x    +    y    =    25   then       y    =    25    -    x  Substitute:            x      2        +          y      2        =    313              x      2        +                  (        25        -        x        )            2        =    313        2          x      2        -    50    x    +    312    =    0              x      2        -    25    x    +    156    =    0              (      x      -      13      )              (      x      -      12      )        =    0  Therefore final answer:      x    =    13    ,    y    =    12        x    =    12    ,    y    =    13

phasiwedi98z · Accepted Answer

Suppose the two numbers are       a  and       b  &quot;The sum of two numbers is 25&quot; gives us:      a    +    b    =    25  &quot;sum of their squares is 313&quot; gives us:            a      2        +          b      2        =    313  The first equation gives us:      b    =    25    -    a  Substituting for       b   into the second we get:            a      2        +                  (        25        -        a        )            2        =    313        ∴          a      2        +    625    -    50    a    +          a      2        =    313        ∴    2          a      2        -    50    a    +    312    =    0        ∴          a      2        -    25    a    +    156    =    0        ∴          (      a      -      12      )              (      a      -      13      )        =    0        ∴    a    =    12    ,    13  The value of       b   corresponding to each solution is now determined using the second equation.      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       12   and       13

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

Answered question

Answer & Explanation

New Questions in High school geometry