\fdO'^ - Old Forge Coal Mines

(d)
Completing the square,
Extracting square root,
Transposing,
{c)
ALGEBRA. 126
x" + Six' - 10 = 22,
or x'" + Six* = 32.
... + 31.-
+(!)' = 3. +
(!)•.
31 33
x" -j- — = ± ir-
^» =__ _|_ _.:::_, or 1.
"^ -
whence, ;r = -i/T= 1
Completing the square,
2 2
-
2 - ^^'
or -* = 4^=732"= - 2. Ans. (Art. 600.)
x^ - 4x^ = 96.
;tr» - 4^' + 4 = 96 + 4 = 100.
Extracting square root, ;tr' — 2 = ± 10.
Transposing and combining, x^ = 12, or — 8.
But, A-' = /P = 12, or - 8.
Removing the radical,
x' = 144, or (— 8)^
f'Tii =VSX'^ = 2vl8. (Art. 538.)
Hence, x = 2^/18, or (— 8)'. Ans.
(236) (a) The value of a' is the same as 1. (Arts.
438 and 439.)
a'
{b) — ^ = a. Ans. (Art. 530.)
{c) 4^(3,1-' + bxf -f {jxyy =1 3.r' 4- 5.r7* + 6,t-> = 3 X 2' + 6
X 2 X 4' -f 6 X 2' X 4 = 12 + 640 + 96 = 748, when x=2,
and ^ = 4. Ans.