35<5 ALCEBRA. 



2. When the square of the unknown quantity Kas any 

 coefficient prefixed to it, let all the rest of the terms be 

 divided by that coefficient. 



3. Add 



la the first form, where ;v=: + -/ d-^-t £., the first valu^ 



42 



z 



of X, vis. ;c=-|-v^ ^4- — — — Is always affirmative ; fof 

 4 2 



^ince J-5 IS greater than — , the greatest square must necessa> 



4 • 4/ 



rily have the greatest square root ; \^ ^-j- _. will, there^i 



4 2 ' 



fore, always be greater than -v/ — > or its equal — ; and cons^ 



quently -t-\/ <^-| — will always be affirmative* 



2 2 ■ ' ■ 



The second value, viz. xzz — t^ ^-j- -i, will always 



42 



be negative, because it is composed of two negative terras. 



Therefore, when x * ■xaxzz.h^ we shall haye x= -J- */ h-\- — — , 



4 



-% 

 5- for the ajHvmative value of ic^ and a;:zz — jJ b-\- i i 



for the negative value of x. 



Jn the second form, where x:=:'^ji/ b-^- ^ -{- JL, the first 



4-2 



value, viz. xzn-^- \f 3 -J- — -j- J5. is always affirmative, since 

 ■ 4 2 



it is composed of two affirmative terms. The second value, viz. 



;)fiz: — y^ ^-(- ^ 4" ~ > ^^^^ always be negative ; for sincQ 

 4 2 ■• ■■,■•■-• 



