ICS

ON CUBIC EQUATIONS

TKACT £8.

104, fix. 3. In the equation x 1 + 18 .r = 6, we bare a~6 yb ~ 3, c = 4/(9 + 216) = \/225 = 15, real, and greater thanb, and therefore this case belongs to the same series as thefc 2 9 1 , Si 6

Z 225 = 23 ~ ‘° 4} aIld V? ~ 2/235 ~

last example. Now

v':

24

35

= £7120 =4/-96.

Then

A

11

^ 1 tf)

!i

•3333333

B

__ 3.5J* _

— 6.9c 3 A “

24692

C

8 . H&* ^ _

~ 12.15c a B “

483

u

14 . iw

~ 18.31c» c ~

12

•3358520 - - - - log', 1-526148©*,'96 ........ 7-9940904

the root x — *3313130 ----- 1-5202384

And then the two imaginary roots are

•331313

± */c . v^-3 X.: !■

w

" 3.6c*

& C.

105. But, in Art. 58, these three roots were found to beyl8-^12, and - ± y/ _ 3 . Consequently

■we have

2 2.5 . S

3.6.25 s

1 +

3 . 6 . 9 . 12.25“

1-5 + 2.5.8.11

&c, and

J /18 + */12

J/18-^12 , 25 __o

£~ V 3 3 ^ 3 . 6.9.25» T 3.6.9.127157251 T- &C *

106, Ex. 4. In the equation x* — l5.r = 4, we havea — - 5, b = 2, and e = -f a 3 ) =^-121 = llv'-l,imaginary, and greater than b, which belongs to the sameseries as the last two examples, hut changing the sign wherethe odd powers of the negative quantity c 1 is concerned, as.in Art. 98.

Now 5 = 17

4 , 2i

12 P and C7» :

=*&• The11