INDETERMINATE PROBLEMS. 207 

 - (*4^)(*-«f) ; whence, x - mz—my, and z+y = »** ; where- 

 fore «z = ^+*. and *= ^ ; alfo, ^ = «*-7 5 conft- 



quently, «j/+* == m-x—my, and J = ^—Jr - " But from the 

 firft equation, y = a — * ; wherefore * — x = — , ana * — 

 m'-k^-i X ^ ' confequently, y = -. +awj _ I , and % _ 



w' + l ., 



m*+2m — 1 



Suppose a == 23, and m zz 4 5 then * = 8, ^ = i5» and z 

 5£ 17. For 8+15 =: 23, and 64+225 == 289 ~ (17)*. 



PROBLEM X. 



To find two numbers, whofe fum pall be a given number , and the- 

 produft of the funis, formed by adding given numbers to them, a 

 fquare. 



By hypothecs, x+y ~ a, and {x+b)(y+c) 3S z\ From 

 the fecond equation, we obtain by affumption, x-j-b = 



mz, and z = my-\-mc ■ therefore, z = -~- = ' rajr+flw: ', and 

 fo x — ot^+otV — b. But, from the firft equation, x zz a—y - y 

 confequently, nfy+mH—b — a—y, and y — " ^foj ' ; alfo x. 



—- ^ — 1/ — £ and £ — — ■ 3*5 • 



Suppose: 



