3<58 AtGEBRAiT 



Or x'-j-y^ =ivy X a—s =rp x a-s: 

 But x^-^-y^zzis^ — pp by the last problem, 



And therefore pxa—s=s^-—^sp by equalityi 

 Or pa—ps -|- 3/j =/ J -\-2pszzs'^. 



a-\-2s 



4.' 



TOience /^4-a— j| — 4/^::if>-f.a— f! ? -- =z5 by sub- 



stitution, 



Or j'4-— j= —11- by reduction. 

 a 2 



And j-rr -^/ 1 [ — — by completing the square, 



and extracting the root. 



And from this vtiiue of / all the rest of the quantities />, X 

 and y may be readily' determined. 



QUESTIONS . FOR PRACTICE. 



I. What two numbers are those, v/hose sum is 20, and 

 their product 36 ? Ans. 2 and 18. 



^ 2. To divide the number 6ci into two such parts, that 

 their product may be to the sum of their squares in the 

 ratio of 2 to 5. Ans. 20 and 4a. ^ 



3. The difference of two numbers is 3, and the differ- 

 ence of their cubes is 117; what are those numbers ? 



Ans. 2 and 5. 



4. A company at a tavern had 81. 15s. to pay for their 

 reckoning ; but, before the bill was settled, two of them 

 sneaked off, and then tUose, who remained, had los. a 

 piece more to pay than before *, how many v/ere there in 

 the company ? Ans. 7. 



