The Academic Algebra

The Academic Algebra

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1889 edition. Excerpt: ... a)n (--6)" if n is even. 198. Like roots of both members of an inequality are inequalities of the same direction. M i i Thus, if a b, then a" 6." In case n is even, the inequality of the possible negative roots is reversed. 199. The sum of the corresponding members of several inequalities of the same direction is an inequality of the same direction. Thus, 7 5 3 2 6 5 CHAPTER XV. INVOLUTION AND EVOLUTION. 203. Involution is the process of raising a number to a power. 204. A number is involved by taking it as a factor as many times as there are units iu the index of the required power. 206. According to Art. 70, (+ a ) X (+ o) = + a1, (+ a) X (+ a) X (+ a) = (+ a2) X (+ a) = + a', and so on; and (--a ) X (-a) = + a1, (-a) X (-a) X (-a) = (+a2) X (-a) =-a', (--a) X (-a) X (--a) X (--a)--(--a8) X (--a) = + a, and so on. Hence, for the signs we have the following Rule. Of a positive number all the powers are positive. Of a negative number the even, powers are positive, and the odd powers negative. INVOLUTION OF MONOMIALS. 206. To raise a monomial to any required power. 1. Find the third p wer of 3 a b. (3 cf-&) =: S rt2 Ifi X 3 a2 ft8 X 3 a2i (1) = 3 3 3 a" a2 a2 6 Ifl 6s (2) = 27a6 (3) According to Art. 204, to raise 3 a2 A8 to the third power, we take it as a factor three times (1); and as it makes no difference in the product in what order the factors are taken, we arrange them as in (2); performing the multiplication ( 72) expressed in (2), we have (3). Hence, Bale. Multiply the exponent of each letter by the index of the required power, and prefix the required potvcr of the numerical coefficient, remembering tJiat t/ie odd powers of a negative number arc negative, while all...
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Product details

  • Paperback | 54 pages
  • 189 x 246 x 3mm | 113g
  • United States
  • English
  • black & white illustrations
  • 1236785479
  • 9781236785473