perplexus.info :: Just Math : Four Square Sum

Four Square Sum (Posted on 2024-05-07)

The sum of the squares of four consecutive integers is two less than a square number.

What is the mean of the four integers?

No Solution Yet Submitted by Danish Ahmed Khan

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Possible Solution

| Comment 1 of 5

(a) The mean of ((x+2)+(x-1)+x+(x+1))/4 = x+1/2

(b) The given equation:

Let (x+2)^2+(x-1)^2+x^2+(x+1)^2=y^2-2

Then 4(x^2+x+2) = y^2 or (2x+1)^2= y^2-7

Let a=(2x+1): a^2=y^2-7,

by inspection, a=+/-3, y==/-4

Then:

a=3, x=1, mean = 3/2

a=-3, x=-2, mean = -3/2

Edited on May 7, 2024, 10:52 am

Posted by broll on 2024-05-07 07:13:47

Please log in:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info