SOLUTION: The difference between 2 natural numbers is 4.The sum of their squares is greater than 9 times sum by 8.Find the numbers

Algebra.Com
Question 825271: The difference between 2 natural numbers is 4.The sum of their squares is greater than 9 times sum by 8.Find the numbers
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
This is somewhat ambiguous, but here is a try.

x and y are the natural numbers to find.
;
.

The sum of just the two numbers can be substituted to give ,


Going back to x+y=4, y=4-x, so substitute into the circle equation:





'
; unless I made a mistake, this value will not be a Natural Number. Neither will be y Natural.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The difference between 2 natural numbers is 4.The sum of their squares is greater than 9 times sum by 8.Find the numbers 


Let the larger and smaller of the 2 numbers be L, and S, respectively

Then: L - S = 4______L = 4 + S ----- eq (i)

Also,  

      

      ---- eq (ii)

       ------ Substituting 4 + S for L in eq (ii)

      

      ______Collecting like-terms

      ______Combining like-terms

      )______Factoring out GCF, 2

      

      (S + 2)(S - 7) = 0

      S = - 2               OR                 S = 7 

Since - 2 is NOT a natural number, the smaller of the 2 natural numbers is: 



L = 7 + 4 ------ Substituting 7 for S in eq (i) 

L = 11, so the larger of the 2 natural number is: 

You can do the check!! 



Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.

Further help is available, online or in-person, for a fee, obviously. 



For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams, 

GENERAL MATH QUESTIONS, MATH HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra,

Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE, GRE, CLEP,

and the GED, you can visit: http://asvabstudyzone.freeforums.net/. 

RELATED QUESTIONS


One number is 2 greater than another number if the sum of the square of their squares is... (answered by Alan3354)

The sum of two numbers is 8 and the difference between their squares is 34. Find their... (answered by rakhileshnaidu,Alan3354)

Find two natural numbers, the sum of whose squares is 25 times their sum and also equal... (answered by Edwin McCravy)

The difference between two numbers is 2, and the sum of their squares is 52. Find the... (answered by jorel555)

hey there thanks ,the question is-
the difference between two numbers is 4 and the sum... (answered by ankor@dixie-net.com)

find two numbers such that their sum multiplied by the sum of their squares is 5500, and... (answered by oscargut)

find two numbers such that their sum multiplied by the sum of their squares is 5500, and... (answered by oscargut)

1. The sum of 4 integers is 24 and their product is 945. What are those integers?

2.... (answered by CPhill,greenestamps)

The difference between two positive numbers is 223 smaller than the sum of their squares.  (answered by richwmiller,ikleyn,greenestamps)