106 
THE APPLICATION OF ALGEBRA 
~ — b (zz 28), will become x 1 —fx zz — 
hence x'—fx + i/* = — ~ + iff, x — \ f = + 
■i/ i/‘ and x = lf±\/if* ~= 16, 
or zz 12; and consequently y (—) — io, or zz 7, 5. 
For j 
i 12 
X 
10 
= 
120 
1 12 
+ 
8 
X 
10 + 5 zz 3 00 
Also ) 
I 16 
X 
7,5 
— 
120 
: 10 
8 
X 
7,5f 5 : 300, 
PROBLEM L» 
To find two numbers, so that their sum, their product, 
tnd the difference of their squares, may be all equal to 
one another. 
The greater being denoted by x, and the lesser by y, 
we have x + y — xy, and x 4- y — x z — y 2 : the last of 
these equations, divided by x + y, gives 1 =r x — y; 
whence x — l + y, this value, substituted for x in the 
first equation, gives 1 + 2y zz y + y 2 ; therefore y 2 —y 
zz 1, and y — \ -f consequently x (1 + y) zz -f 
PROBLEM LI. 
To divide the number 100 faj it\to two such parts, 
that the sum of their square roots may be 14 fbj. 
Let the greater part be x, and the lesser will be a—x; 
therefore, by the problem, \/x + \/a — a- zz b; and, 
by squaring both sides x-p Vs/ax—xx -P a— x zz bb; 
whence, by transposition and division, s/ax —xx zz 
: therefore, by squaring again, ax — xx zz 
or x z 
bb — öl’' 
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