10* 
THE APPLICATION OF ALGEBR4. 
the question, 50 4 x x 50 — x, or 2500 — x* — 2100; 
whence x z zz 400, and consequently x — \/400 =: 20; 
¿herefaEe 50 4 x — 70 — the greater part, and 50 — x 
zz 30 = the less. 
PROBLEM XL, 
Whqt two numbers are those which are to one another 
in the ratio of 3 fa) to 5 f'bj, and whose squares, added 
together, make 1666 (c) ? 
Let the lesser of the two required numbers be a*» 
boo 
then, a : b :: x : —— rr the greater; therefore, by 
b*x z 
the question, x 1 q—— c; whence a 1 x 1 4- 6 a a* zz aV, 
a* zz -0-771»; consequently a’ = 
a* 4 b* 
the greater. 
PROBLEM XLI 
To find two numbers, whose difference is 8, and pro» 
fact 240. 
If the lesser number be denoted by x, the greater will 
be x 4 8 ; and so, by the question, we shall have a* 4 8x 
240. Now, by completing the square, x 1 4 8a 
4- 16 240 4 16) = 25G; and, by extracting the 
root, x 4 4 =r s/256 = 16: whence x — 16 — 4 zz 
12; and x 4 8 = 20; which are the two numbers that 
were to be found. 
PROBLEM XLI I 
To find two numbers whose dfference shall be 12, and 
the sum of their squares 1424. 
Let the lesser be a, and the greater will be x 4 12; 
therefore, by the problem, x 4 12 j 1 4 x z zz 1424, or