INDETERMINATE PROBLEMS. 207 

 rr (z-{-j')(2 — y) ; whence, x^=. trvz — ay, and 2+v = mx ; where- 

 fore mz =. my+x, and z = — — ; alfo, z — mx—y ; conf'Q' 



m X — V 



quently, iny-\-x iz: m'^x — my, and y zz — — — • But from the 

 firft eqviation, y =. a — x ; wherefore a — x z=. — ^— , and x z=. 



2m _ »i* — I J 



— —, Xa; conlequently, v =: — rr. » ^^^ ^ — 



-Xa. 



CT*+2m — I 



Suppose a zz 23, and m zz 4 ; then x zz S, y :z: i^, and z 

 zz 17. For 8+15 = 23, and 64+225 = 289 -— {17Y' 



PROBLEM X. 



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

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

 fquare. 



By hypothefis, x-^y zz a, and {x-\-b)[y-{-c) — z\ From 

 the fecond equation, we obtain by aflumption, x-^-b zi 



mz, and z zzz my-\-mc ; therefore, z zz —^ — zr ' my-\-mc ; and 

 fo X zz my-\-?n'^c — b. But, from the firft equation, x =z a — y ^ 

 confequently, m'^y-\-m'^c — h zz a — y, and y zz ^^, ; alfo x. 



zz a—y - IHll+ffl^'', and z rr ^±^ - J!I2±£l+tL. 



Suppose, 



