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Integer Solutions (Posted on 2006-03-30) Difficulty: 3 of 5
Determine all integer solutions (x,y,z) for the system of equations

x²z + y²z + 4xy = 40,

x² + y² + xyz = 20

See The Solution Submitted by Bractals    
Rating: 2.5000 (6 votes)

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Solution KISS | Comment 8 of 16 |

LET

X^2+Y^2=W  AND XY=T

WE GET:      W+4T=40             (1)  error  -please  see            my later post  i.e.      COMMENT# 15

AND             W+TZ=20            ( 2)

SUBTRACT   (1)-(2)====>  T*(4-Z)=20

CHECK FOR  T =  1,2,4   ...20, -1,....-20  /divisors of 20/

TO FIND ALL INTEGER SOLUTIONS 

GO BACK TO FIND X,Y,Z  (X AND Y ARE INTERCHANGABLE)

ady

Edited on March 31, 2006, 12:21 am

Edited on April 1, 2006, 3:54 am
  Posted by Ady TZIDON on 2006-03-31 00:20:23

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