The book Graphs was written by author Robert J Robert Judson Aley Here you can read free online of Graphs book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Graphs a good or bad book?
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Simultaneous Quadratics.
17 Equations (i) and (2) give a straight line and the double-branched curve known as the hyper- bola. These intersect at the points P, Q, whose 0\ i^ < cs-r ^^s-r- / Fig. 16.
coordinates are (-3, 5) and (5, - 3). These are the only solutions to the system of equations. The auxiliary lines (3) and (4) intersect line (i) in P and Q, and hyperbola (2) in R and 5.
\. Xy = 12.
2. X^ -\- y^ = 40.
The auxihary equations appearing in the solution are : 3. Jr-f j/ = + 8.
4. X -^y = -^.
5. X—y = ^A, .
6. A'-j = -4.
i8 Graphs.
The graphs of all these equations are shown in Fig. 17 by the corresponding numbers.
The solutions are at the points -P, Q^ R, and 5.
Y Fig. 17.
The Complex Number.
In making general the treatment of quadratics, the complex number becomes necessary. The imaginary unit or z( = V— i) appears in the extraction of the square root of a negative quan- tity. E. G. , V — 4 = V4 ( — I ) = V4 • V — I = ± 2 V— I =±22.
a + bi is the type of all complex numbers.
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