2o8 O/i the RESOLUTION of 



Suppose a — ly, b z=. 6, c — 2, and let m — 2 ; then y 



_ 17+'^— 8 ri8+S_6 , 34+4+12 



- 4+1 - 3. ^ = —Tr = H.andzr:^-— = 10. 

 But 14+3 zz ly, and (i44-6)(3+2) = 100 = (10)'. 



PROBLEM XI. 



Let it be required to find two numbers, fuch that, if to each, 

 their fum and difference, unit be added, the numbers refulting fiiall be 

 fquares. 



The firft condition will be obferved, if the numbers be de- 

 noted by x^ — I andj-^ — I. The hypothefis will then require 



K'^+y^ — I = x% and x^— j/^+i =. v"-. 



Transposing the firft equation, x^ — i = 2^ — ■/*, and re- 

 folving into fadtors, {x+\)[x — i) = {z+y){z — y); whence, 

 v+ 1 = mz — my, and z-\-y z=. mx — m ; therefore, z = mx — m — y 



-, from which we have y = 



"'.V+-^+r ,- , , , , _ ,„.^_^_„,x_i 



2m 



Again, tranfpofing the fecond equation, x^ — -j* = v'' — i, 

 and refolving, {x-\-y){x—y) = [y-\-i){v — i), and by aflumption, 



x-\-y = pv — p, and v-\-i =. px — py, and therefore, v =: 



px—py-i = -i-!2:l^. Hence y = ^'^-^^ . 



But it was found, that y = "''«— ^— >"'— j . wherefore, »■ 

 - ^'^71"'^ _ ,.'^-.-,.^-1 ^^^ ^ redudion, x 



