43 ® Dr. button on Cubic Equations 
104. Ex. 3. In the equation * 3 + 18# = 6, we have 
<7 = 6, b. — 3, c ~ ■>/ Q 4- 216 — \/ 2 a 3 ~ i'5> real and 
greater than < 5 , and therefore this cafe belongs to the fame 
feries as the Taft example. Now - 
9 - _ 1 
“5 25 
04, and; 
2(5 __ 
~$ c % 4/245 
= ,\/'g 6 » Then-. 
B = 
3 
2 . 5^ 
6 . 9 c 
8 . 1 1 b z 
G = — ; B = 
12 . 15 c’ 
14.17 b % ' 
2 5 5 
- •3333333 
A = 2469?.: 
483; 
l8 . 2.1 C 
12 
•335852° - log- x*526i48o- 
^•96 7-9940904 
the root # = ’331-3130 - - 7*5202384 
And then the two imaginary roots are 
—'111111 ±- J/c , V - 3 x m & e . 
2 u 3 . 6c 
105. But, in Art. 58, thefe three roots were found 
to be V i 8 — ^/i 2, and - - — — ± - — v-3.. 
Confequently we have 
^iS + v'j* 
= X - 
*^»s 
4/78 — 4/12. 3 y/25 
— — — - — - &c. 
3.6. 25* 3.6.9. 12 . 25* 
= ~ +• 
2 • 5 
n + 
2.5. 8 . 1 1 
3 3.6.9.25* 3 . 6 . 9 , 12 . 15 . 25 
? + &e. 
1 06. EX 
