3^2 ALGEBRA* 



7. Givai X* — axm — 3 •, to find x. 



Ans. a:zz + ^ if -j . 



-^4 ^ 



g 



8. Given --— r+'~7 =: -7- ; to find .v. 



if a f h 



9. Given a^v* — ,y* -[-104=1600 5 to find x. 



Ans. .v=ii:4. 



± p r 



10- Given q.v" — 2a;" — ~ zz — ; to find .v. 

 ^ 99 



A„s.«=±s/^-±^ + l 



QUESTIONS PRODUCING ^ADRATIC E^JATIONS. 



1. To find two numbers, whose di^erence is 8 and 

 product 240. 



Let X equal the less number, 

 Then will ^i'-j-S equal the greater. 



And xy^x-^^zzx"^ -^Zxziii^o by the question ; 

 Whence x"" ^^x-\-i6z=:i2^o^i(>-=z2^6 by completing 

 the square j 



Also A^-|-4 1=^/25 6= 16 by evolution ; 

 And therefore xzniO — 41=12= less number, and 12-J-8 

 1=20:::= greater. 



2. To divide the number 60 into two such parts, that 

 their product may be 864. 



Let X zz greater part, 



Then 



