Essentials of Algebra (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1897 Excerpt: ...term of the root, we obtain the complete divisor, 3 a2 + 3 ab + 62. Multiplying this by 6, and subtracting the product, 3a26 + 3a62+63, from the remainder, there are no terms remaining. From the above process, we derive the following rule: Arrange the expression according to the powers of some letter. Extract the cube root of the first term, write the result as the first term of the root, and subtract its cube from the given expression; arranging the remainder in the same order of powers as the given expression. Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root. Add to the trial-divisor three times the product of the term of the root last obtained by the part of the root previously found, and the square of the term of the noot last obtained. Multiply the complete divisor by the term of the root last obtained, and subtract the product from the remainder. If other terms remain, proceed as before, taking three times the square of the part of the root already found for the next trial-divisor. EXAMPLES. 201. 1. Find the cube root of 8;--36 aty + 54arV-27 f. 8x6-36x48/ + 54xV2-272/3 2x2-3y, Ans. 8ofi The first term of the root is the cube root of 8 x6, or 2 x2. Subtracting the cube of 2x2, or 8X6, from the given expression, the first term of the remainder is--36 xy. Dividing this by three times the square of the first term of the root, or 12 x1, we obtain the second term of the root, --3y. Adding to the trial-divisor three times the product of the term of the root last obtained by the part of the root previously found, or--18 x2y, and the square of the term of the root last obtained, or 9 y2, we have the complete divisor, 12 x4--18 x2// + 9y2. Multiplying this comp..