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#