TRACT 28.

AND INFINITE SERIES.

113

115. But, by Art. 62, these same three roots are, — 3, and; which being compared with the series belonging tothis case, we find

-|- &c, and

— &c.

2 . 81

yg = i -f

12^/350 v T 3 . 6 . 175

V 21 ~ 3 3 /3SO = —

36 3 3.6.9. 175

2.5.8. 81*

3.6.9 . 12.175 22.5 . 81 . 2.5.8.11 . 81®

+ ;

3 . 6 . 9 . 12.15 . 175 2

116. Ex. 8. In the equation x' s — 12.r = — 8^/2, we havea= — 4, b = — 4^/2, and c 2 = 32 — 64 = — 32; which beingnegative, and equal to 6 2 , the three roots will be found, byboth the forms of series, like as in Ex. 5, Art. 109; butthe operation is here omitted for the same reasons as werethere given. The three roots of this equation were, inArt. 63, found to be 2^/2 and — v /2± v /6.

117. Ex. 9. In the equation x 3 — 15# = 22, we havea = —5, 6=11, and c 2 = 121 — 125=—4*; which beingnegative, and less than 6% the series in Art. 68 give thesethree roots:

2c a 2.5.8c 4

Greatest .

toot — ~\/11 x : 1 -}

&c, and

_ 3

the twoless roots

HereA =

B =

i/ilx-.l

. W * • 1 .

V121 ' 3

3.6.9. 125 42.5, 8c 4

3.6 i 2

where

3 . 6i 22.5 c 2

3.6.9. 125 42.5.8. lie 4

3 . 6 . 9i 2

6.9.12.154 4

B =

2c 2

3.6 ii 211 . 14c 215 . 186 2

= 1'0000000= 36731

c =

8

c =

5.8c 29 . 124 2

B =- -00004*50

+ 1-0036739- 0-0000450

1- 0036289

2

2- 0072578

i/n

the greatest root = 4-4641016VOL. II.

- - - - log. 0-3026031. 0-3471309

0-6497340