\fdO'^ - Old Forge Coal Mines

Completing the square,
ALGEBRA. 131
x" - ^abx + Aa^b'' = a* -\- 2a* b^ + b\
x-2ab= ± {a' -\- b').
x={a'-^2ab-\-b'),
or- {a^.-2ab-\-b*).
x={a + by, or -{a — by. Ans. Ill
'
(b) y 4- = ,
, , becomes
'' V^+l l/JUT ^x'-l
— Vx — 1 + V^-\- 1 = 1 when cleared of fractions.
Squaring,
X-1 — - 2i/-r' 1 ;ir + + 1 = 1.
— - 24/^' 1 = 1 - 2;ir.
Squaring again,
Canceling 4;r' and transposing,
4jr' — 4 = 1 — 4^: -j- 4ar".
4;jr= 5.
;r = - = 1- Ans.
4 4
(230) 5;ir - 2j = 51. (1)
19a' - 3j = 180. (2)
We will first find the value of ;ir by transposing — 2j to the
second member of equation (1), whence 5x = 51 + 2y, and
- = 5i±^. (8)
This gives the value of x in terms of f. Substituting the
value of X for the x in (2), (Art. 609.)
19(51 + 2f)
5
3/ = 180.
T^ J- 969 + 38
^y Expandmg, 3j = ^
180.
Clearing of fractions, 9G9 + 38j — 15^ = 900.
Transposing and uniting,
23j = — 69.
J = — 3. Ans.
Substituting this value in equation (3), we have
X =—z— = 9. Ans.