QUADRATIC »E(^ATIONS. 363 



Then will 60 — Xzn less, 



And k)<6o — x:=6ox — x'z:z^6^ by the quesfi^n, 

 That is, X' — 60XZZ — 864; 

 Whence iv' — 6ox-\-90o= — 3644-9^'=^3^ ^Y complet- 

 ing the square ; 



Also X — 30ZZY/30— 6 by extracting the root ; 



And therefore .\rz:6+3c— 3'v'5z=: greater part, 



And 60— ;czz6 — 36^124= less. 



3. Given the sum of two numbers =:io(//), and the 

 sum of their squares =58 (^) 5 to find those numbers. 



Let x=: greater of those numbers, 

 Then will a — xzz less *, 



And AT^+rt— A'j ZZ2X'']'a'^ — 2nxz=.h by the (question, 



Or ;v* + ax=.— by division, • 



* 2 2 ^ 



h a"- h—a^ 



Or »Y*— .7.v=r T— zz. — : — by transposition 3 



22 2 "^ 



Whence x ' — ax A zz: A rz: • by com^ 



4 2*4 4 



pleting the square. 



Also X = </ by extractmg the root ; 



2 ■ 4 



And therefore ^:=+\/ J— -4- — z:: greater number, \^ 



42 N. 



a 2b — a* — 2b— a'- a 

 And a A-^ = 4. v/ * 4 =: less, 



'^ 4 42 



Hence these two theoVcms, being put into numbers, give 

 7 and 3 for the numbers required. 



4. Sold a piece of cloth for 24I. and gained as much 

 per cent, as the cloth cost mc ; what was the price of the 

 cloth ? 



Let 



