Expert: Paul Klarreich - 7/24/2009

Question
Hi,
Let x and y be positive integers such that x^2 + 3x +y^2 = 404. What is the value of x + y^3? Find all possible solutions.

How can I solve this using Excel (I have never used Excel for maths before, so I need some background information).

Thankyou very much,

Tim

Answer
Questioner: Tim
Country: Australia
Category: Advanced Math
Private: No
Subject: Problem using MS Excel
Question: Hi,
Let x and y be positive integers such that x^2 + 3x +y^2 = 404. What is the value of x + y^3? Find all possible solutions.

How can I solve this using Excel (I have never used Excel for maths before, so I need some background information).

Thankyou very much,

Tim
........................................
I am not sure what your question asks -- is  x + y^3 always the same number?  I don't think so.

However, a couple of things stand out:

If x^2 + 3x +y^2 = 404,

AND, since x^2 + 3x is always even, y^2 is always even.

Since 20^2 is 400, you can conclude that the possible values of y are only 2,4,6...,20.

Now try each and solve for x.  For example:

y = 20:  x^2 + 3x + 400 = 404

x^2 + 3x - 4 = 0

(x + 4)(x - 1) = 0

x = 1.

y = 18:  x^2 + 3x + 324 = 404

x^2 + 3x - 80  = 0

Does not factor; no integer solutions.

Etc.  Only 8 more to try.

I have used Excel, but I am not an expert on using it.