SOLUTION: The difference between the squares of two numbers is 21. Three times the square of the first number increased by the square of the second number is 79. Find the numbers.

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Question 1158710: The difference between the squares of two numbers is 21. Three times the square of the first number increased by the square of the second number is 79. Find the numbers.
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between the squares of two numbers is 21. Three times the square of the first number increased by the square of the second number is 79. Find the numbers.
--------
Assuming they're integers:
---
a^2 - b^2 = 21
(a-b)*(a+b) = 21
---> 3 & 7
=============
a - b = 3
a + b = 7
--------------- Add
2a = 10
a = 5
b = 2
----
Also -5 and -2
============
3a^2 + 2b^2 = 79
---------
===============
The "hard way:"
a^2 - b^2 = 21
3a^2+ b^2 = 79
--------------------------- Add
4a^2 = 100
etc
Not much harder.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let the numbers be x and y. Then the given information is

x%5E2-y%5E2+=+21
3x%5E2%2By%5E2+=+79

It should be obvious what method to use to solve the pair of equations; adding the two equations eliminates y.

4x%5E2+=+100
x%5E2+=+25
25-y%5E2+=+21
y%5E2+=+4

We know the square of one of the numbers is 25; but there is no information that lets us determine whether the number is 5 or -5.

Likewise, we know the square of the other number is 4; but we can't tell if that number is 2 or -2.

So we can only say that the two numbers are 5 or -5, and 2 or -2.