quadratic, cubic, quadrato^cubic, and higher Surds. 39 
Therefore ^ 5 a^ifc^ — 7 "\/ a^b^c^ -f 4 abc^ ==■ 
— 771 ( = — ) Multiply by y ; 'V — y c "\/ u^b^c^^ 
+ ±c^ ^^Va^bY^ — ~ Wahc^ = — -i- 
’5 5 5 
Put, ”\/ ^266^ = X + — ^ ; then, 
Z^4- ~ ^:jc^+ — c''x''-}~ 
1 ^ • 200 ' 
343 ,3 
2000 
C^X-{‘ - P -- - - c* 
* lOOOOO 
5 
100 2000 
4- — + — c^x + ^ c* > 
I 5 * 25 ' 500 
40000 
H . 3 ^ I 49 
— C^X 
5 
^ c‘ 
100 
I 
4 . ^ + 
• 200 ' 
2723 
JI- 
iOOO 
C ♦ 
c3x =0. 
-|--^c37n 
+ y ^^771 _ 
To solve this biquadratic equation, substitute in the equation, 
— _2^(^3 
* ~P' z + 7 ^^ = 0, for <7, — r ; for r, -dd- ; and for s, 
— 45 . ,•» 2 13 200 ’ ’ 1 000 ’ ’ 
■ — c* j- ch 7 i : then, z^ * ^ 4. = 0 : 
lOOCOO • 5 » — ^ +T7T^ 
j ' '~ ' ' ' ' 
•.* js — ^ c d — — c‘^m-\- \c^ 1362Ic'^ — \6/^y//^c'^m-\-66\6i()c^nC' — 864000cm* 
15 2 2 
-j- ”C — ^-^c*m— -|c^ 1 3621 c'*’ — i64574c^/?i-f 661 689c’’m’'— 864000cm* 
then, jr = -f 
I 1 / 
^ + X 
300 — ^ 
.v/ 
— Cf — / 
150 -r^ 
17 
500 
a 
JS — - c 
300 
.v/^ 
17 
500 
or, X = + i ^z — — + — s; c^ 
> — 2 200—2 150 w fj 
r 2 — . — 
2 c* 
300 
abc^=. d~c-\- 
= Z , + xl/*_ il ^ 
20 '2 joo — ^ 15 *^ 
■Z^—C^-\ 7 
150 ' \/ 
17 
500 
13 - 
« — . C 
3oo 
+ — 
» 20 — ^ 300 — 2 1^0 |/ 13 
.y 
17 
500 
2T— ~C' 
800 
