64 ON THE ALGEBRAICAL SOLUTION OF 



. (3) 



Adding now corresponding sides of (2) and (3) and omitting 

 the terms which are common to both sides we obtain 



For example, X 1 =x 2 =y 2 =l 9 2/ x =2 gives 



2 4 +8 4 -l-18 4 +33 4 =6 4 +14 4 +24 4 +31 4 . 

 Again, we have identically 



Multiplying corresponding sides of these equations together 

 we obtain 



which is an algebraical solution of the equation 



P 1 4 +P 2 4 +P 3 4 +^4 4 +^5 4 



Again, we have identically 



+ 1 



, 



2* 1 4 +y 1 44 



Hence by subtraction we get 



>. 4 i 4\4 /0~ _4_ 4\4 /0. 4_. y 4\4 



44 24 / 2\4 



_\ 

 2 * 



A1 



' 



