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) (Show Source): You can put this solution on YOUR website!
1.
2.
From 1,
Substituting,
So the two integers are 14 and 21.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
let integers be and
if they have a sum of , than ....eq.1...solve for
if the sum of their squares is , than we have ....eq.2
....substitute
...simplify
....factor
solutions:
->
or
->
find :
if -> ->
if -> ->
so, your solution is:the numbers and
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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.
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