IN THE HIGHER ALGEBRA. 135 
and, by means of symmetric functions, we are conducted to, 
Ni) fl) =2c+ (wz +y), f@) -f@)=2b + (wz +y). 
It follows from this, that 
@=-5(a@z+y — 2)? 
or, eliminating vz and reducing by the aid of (12), 
@-5*(3y+1)=0, 
whence, permuting and determining the symmetric func- 
tions by means of (12), 
RD 7 
g425'9, 5 
which verifies (9). 
§ 14. 
Again, let 5Q=1 and E=O and replace 2, w, 2, y, z 
by 1, 7, 7”, 0, O respectively, 7 being an unreal cube root 
of unity. Then 
SO JMO=HF, [QO FOYH=9, 
and, consequently, 
0=bcj, or 64+57=0, 
whence 
(7? + 5°)?=0, 
Developing this equation, and comparing its coefficients 
with those of (3), we have 
2, or, B=2:5' 
4 
ee ra) val eV Jae 
as before. 
§ 15. 
The equation (11) may be put under the form 
(6° + 5°QH@ + 5’Q*)?=5"(108Q°E — E*)0, 
and this may be readily transformed into 
(9°+AS?-+ B)?= Cs, 
or 
