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Ray's Algebra Volume 2; Designed for High Schools and Colleges. an Analytical Treatise

Ray's Algebra Volume 2; Designed for High Schools and Colleges. an Analytical Treatise


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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. 1852 Excerpt: ...is ax1--bx=c. Every equation of the second degree containing only one unknown quantity may be reduced to one of these forms. For, in the case of an incomplete equation, all the terms containing x2 may be collected together, and then, if the coefficient of x1 contains more than one term, it may be assumed equal to a single quantity, as a, and the sum of the known quantities to another quantity, b; and the equation then becomes, ax=b, or ax2--6=0. A complete equation may be reduced in like manner; for, all the terms containing x2 may be reduced to one term, as or2; and those containing x to one, as bx; and the known terms to one, as c; the equation then is, ax7--bx=c, or ax--bx--c=0. Hence, we infer, that every equation of the second degree containing only one unknown quantity, may be reduced to an incomplete equation containing two terms, or to a complete equation containing three terms. Frequent illustrations of these principles will occur hereafter. INCOMPLETE EQUATIONS OF THE SECOND DEGREE. Art. 227. 1. Let it be required to find the value of x in the equation, x2--34-ts2i3=12---x3. Clearing of fractions, 4x2--36]5x2=153--12x2; Transposing and reducing, 21x2=189; Dividing, x=9; Extracting the square root of both members; x= 3, that is, x=+3, or x=--3. Verification. (+3)2_3+/3(+3)2=12--(+3)'. or, 3--3+3=12--9; 33=31. 4 4 Since the square of--3 is the same as the square of +3, the value x=--3, will give the same result as x=--3. 2. Given ax2+6=d+cx2, to find the value of x. Transposing, ax1--cx2=d--b; Factoring, (a--c)x2=d--6; Dividing, x5=; a--c -j6 a--c W From the preceding examples, we derive the following Rule Fob The Solution Of An Incomplete Equation Of The Second Degree.--Reduce the equation to the form ax=b. Divide by the coefficient of x2...


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Product Details
  • ISBN-13: 9781236041487
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 80
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1236041488
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 159 gr


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Ray's Algebra Volume 2; Designed for High Schools and Colleges. an Analytical Treatise
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