SOLUTION: 2 integers have a sum of 35. The sum of their squares is 637. Find the numbers.

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Question 1085089: 2 integers have a sum of 35. The sum of their squares is 637. Find the numbers.
Found 3 solutions by Fombitz, MathLover1, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
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1.A%2BB=35
2.A%5E2%2BB%5E2=637
From 1,
A=35-B
Substituting,
%2835-B%29%5E2%2BB%5E2=637
B%5E2-70B%2B1225=637
2B%5E2-70B%2B1225=637
2B%5E2-70B%2B588=0
B%5E2-35B%2B294=0
%28B-14%29%28B-21%29=0
So the two integers are 14 and 21.


Answer by MathLover1(20849) About Me  (Show Source):
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let 2 integers be x and y
if they have a sum of 35, than x%2By=35....eq.1...solve for x
x=35-y
if the sum of their squares is 637, than we have x%5E2%2By%5E2=637....eq.2
x%5E2%2By%5E2=637....substitute x=35-y
%2835-y%29%5E2%2By%5E2=637
1225-70y%2By%5E2%2By%5E2=637
1225-70y%2B2y%5E2=637
1225-637-70y%2B2y%5E2=0
2y%5E2-70y%2B588=0...simplify
y%5E2-35y%2B294=0....factor
y%5E2-21y-14y%2B294=0
%28y%5E2-14y%29-%2821y-294%29=0
y%28y-14%29-21%28y-14%29=0
%28y+-+21%29%28y+-+14%29+=+0
solutions:
%28y+-+21%29=+0->y=21
or
%28y+-+14%29+=+0->y=14
find x:
x=35-y if y=21 ->x=35-21 ->x=14
x=35-y if y=14->x=35-14 ->x=21
so, your solution is:the numbers 14 and 21


Answer by Alan3354(69443) About Me  (Show Source):
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2 integers have a sum of 35. The sum of their squares is 637. Find the numbers.
----------
35 = 5*7
637 = 13*7^2
----
--> 2*7 & 3*7
= 14 & 21
=====================
The long way:
x + y = 35 --> y = 35-x
x^2 + y^2 = 637
Sub for y
x^2 + (35-x)^2 = 637
2x^2 - 70x + 1225 = 637
2x^2 - 70x + 588 = 0
x^2 - 35x + 294 = 0
(x-14)*(x-21) = 0
etc.