SOLUTION: The sum of the squares of two consecutive positive integers is 61. Find these two numbers

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The sum of the squares of two consecutive positive integers is 61. Find these two numbers      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 973375: The sum of the squares of two consecutive positive integers is 61. Find these two numbers
Found 2 solutions by macston, Alan3354:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
x and x+1 are consecutive integers
x%5E2%2B%28x%2B1%29%5E2=61
x%5E2%2Bx%5E2%2B2x%2B1=61
2x%5E2%2B2x=60
x%5E2%2Bx=30
x%5E2%2Bx-30=0
%28x%2B6%29%28x-5%29=0
x%2B6=0 or x-5=0
x=-6 or x=5
The first positive integer is 5.
x+1=5+1=6 The second integer is 6.
.
CHECK:
x%5E2%2B%28x%2B1%29%5E2=61
5%5E2%2B6%5E2=61
25%2B36=61
61=61

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the squares of two consecutive positive integers is 61. Find these two numbers
--------------
61/2 = 30.5
sqrt%2830.5%29 =~ 5.5
--> 5 & 6