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12. If ab(x? – yo)+ xy(a? – 62) 1
(a? +62)(2x2 + y2) Then (a? +62)(x2 + y2)>2ab(x2 - y2)+2.ry(a'-62),
and (a? - 2ab +62)x2 + (a? + 2ab +62)y2> 2xy(a? – 62);
.: (a−b)2x2 – 2(a - b)(a + b)xy + (a + b)y->0. .. (a - b)x - (a +b)y>0; (a - b)x> (a + b)y; and
a+b _ (a")"+(6x)"_**+y* 5.
which is of the forms Section IV., Art. 13, p. 22. ?
x+y a" to (a)+(6") amn+bmn_(am)"+(b*)m_2"+y+
not of the required forms, except when m=r, a+b (a")+(6") x+y an+"
a” –b"_"Ły. ap+bA P a artu
1 6. a"-3"=a-(8m)*=an – 2cm. am-b=am - (31*)=a"-3.
Here a"- 200 and am - 2m have a common divisor when m and n are odd or even numbers. 7. Let am – 3"=(am) – (0*)=x-Y ; 1
1 then an – bm=(am) m* — (64) mn=2"*- ymm, and the given expressions are reduced to the
forms a-6 and a" – 6".
9. Since x=7,.=,...
ELEMENTARY ARITHMETIC, WITH BRIEF NOTICES OF ITS HISTORY.
In Twelve Sections, demy 8vo.
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SECTION I. Of Numbers, pp. 28
3d. SECTION V. Of Logarithms, pp. 16
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