The sum of two numbers is 25 and the sum of their squares is 313. How do you find the numbers?

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Answer 1 · 2018-03-02T09:54:36

$12$ and $13$

let,the two numbers be $a$ and $b$ ,

So, $a+b=25$

and, $a^2 +b^2 =313$

Now, $a^2 +b^2 = (a+b)^2 -2ab$

so, $313=625-2ab$

so, $ab=156$

Now, $(a-b)^2 =(a+b)^2 -4ab$

or, $(a-b)^2 = 625-624=1$

So, $(a-b) = _-^+ 1$

So, we have, $a+b =25$ and, $a-b=_-^+1$

Solving both we get, $a=13.b=12$ and $a=12,b=13$

So,the numbers are $12&13$