Author:
Various Authors

Published: 1911

Language:
English

Wordcount:
201,686 / 622 pg

Flesch-Kincaid Reading Ease: 75.8

LoC Category: AE

Downloads: 886

Added to site: 2011.08.21

mnybks.net#: 30626

Genre: Reference

Excerpt
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an be given, and the solution of any particular problem will largely depend upon the student's ingenuity. Here we shall only give a few typical examples.

*1.* Equations which may be reduced to linear equations.--Ex. *To solve x(x - a) = yz, y(y - b) = zx, z(z - c)=xy. Multiply the equations by y, z and x respectively, and divide the sum by xyz; then*

*a b c -- + -- + -- = 0 ... (1). z x y*

*Multiply by z, x and y, and divide the sum by xyz; then*

*a b c -- + -- + -- = 0 ... (2). y z x*

*From (1) and (2) by cross multiplication we obtain*

*1 1 1 1 ----------- = ----------- = ----------- = -------- (suppose)(3). y(b^2 - ac) z(c^2 - ab) x(a^2 - bc) [lambda]*

*Substituting for x, y and z in x(x - a) = yz we obtain*

*1 3abc - (a^3 + b^3 + c^3) -------- = ------------------------------; [lambda] (a^2 - bc)(b^2 - ac)(c^2 - ab)*

*and therefore x, y and z are known from (3). The same ar*