SOLUTION: two numbers differ by 7 and the sum of their squares is 29. find the numbers

Algebra.Com
Question 298382: two numbers differ by 7 and the sum of their squares is 29. find the numbers
Found 2 solutions by JBarnum, Stitch:
Answer by JBarnum(2146)   (Show Source): You can put this solution on YOUR website!


Answer by Stitch(470)   (Show Source): You can put this solution on YOUR website!
Set-Up
--------
Equation 1:
Equation 2:
Solution:
----------
Plug (B+7) into equation 2 for A
Equation 2:
Expand
Combine like terms
Subtract 29 from both sides
Factor out a 2 on the left side
Divides both sides by 2

----------------
Find the factor of 10: 1,2,5,10
2 & 5 fit the equation
rewrite teh equation
There are two answers to solve for.
---------------


---------------


---------------
Note that sice you have 2 B values, you will need to find 2 A values
Plug the B values into equation 1 to find A
Equation 1:
----------------------


----------------------


So you have two solutions:
The numbers can be -5 and 2
or they can be -2 and 5

RELATED QUESTIONS

two positive numbers differ by 7 and the sum of their squares is 169. find the numbers. (answered by Tatiana_Stebko)
two numbers differ by 2. The sum. of their squares is 244.find the numbers (answered by addingup,MathTherapy)
Two numbers differ by 7,the different of their squares is 91,find the... (answered by ankor@dixie-net.com)
two numbers differ by 8 and the sum of their squares is 320. find the two... (answered by drk)
Two positive numbers differ by 5 and the squares of their sum is 169. Find the... (answered by sofiyac)
two numbers differ by 9. the sum of their squares is 653. what are the... (answered by josgarithmetic)
Two positive numbers differ by 6, and their squares differ by 96. Find the... (answered by ankor@dixie-net.com)
Two numbers differ by 3 . The sum of their reciprocal is 7/10 find the... (answered by stanbon,josmiceli)
two positive numbers differ by 4 and square of their sum is 324. Find the... (answered by josgarithmetic)