Refolution of Algebraical Equations. 
9 
ft in 2 ft 
above-mentioned quantity = a =a"p+b”p” z + yib ,pi " I + 
2 n n n 
yilblpl. 
6. II. Let n be an even number, not divifible by 3, 
then will x n — na z bpx n ~ % + n. a*b z p 1 x r ‘~ i — n. n -~ . 
n — ir n — 12 n — 13 
2 3 4 
alb l p % x n -' i + a*byx”- 11 - n. 
—If a 10 byx n ~ ls + n.- a' 1 bf b x n ~ l% - 
5 * 3 4 5 6 
n n n 
&cc. to terms as before — b~p ~~ 1 (2XT + L n ,’Lz± 
a z bpx^~ 2 +- } xn. aWp z xi ~ 6 + L x *. . 
J 2* 234 2 5 2 3 
7 f +- i 2 jn — 14 0 — 16 9,1 „„ 0 — 10 0— 12 * — 14 n — 16 n — iB 
, . # P&x* +—.-x n. — - — — • m 
4 5° 2 23456 
« — ■ 20 n — 22 
*72 2 
g a*byx.z ~ 11 + 8cc.)~a — a”p-b”p n 
Let a be an even number divifible by 3, then will 
in n n 
the above-mentioned quantity h-a n p-b n p n ~ 1 - ylbTpl + 
a in zn * 
yjblp‘i~\ 
In air the preceding cafes n, in and r denote whole af- 
firmative numbers. 
Thefe equations may be deduced in the fame manner 
as is before given in Cafe 3. 1 ; or can be demonftrated 
by writing in the equation free from radicals for the dif- 
ferent powers of x their values deduced from the given 
equation x= a\/p + btfp n 
% 
