A Short Course in College Mathematics, Comprising Thirty-Six Lessons On Algebra, Coordinate Methods, And Plane Trigonometry
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In our eReader you can find the full English version of the book. Read A Short Course in College Mathematics, Comprising Thirty-Six Lessons On Algebra, Coordinate Methods, And Plane Trigonometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Short Course in College Mathematics, Comprising Thirty-Six Lessons On Algebra, Coordinate Methods, And Plane Trigonometry
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Here A = 9,\, B = 216, hence iJ/(4 A) = 216/(4 x 81)= f. Substituting X = x — | in the above equation we obtain the new equa- tion 81 X* — 729 x2 - 162 X + 810 = 0, or, dividing through by 81, x< - 9 a;2 — 2x -1-10 = 0. The roots of this equation were found in 15.9 to be - 2.60, - 1.32, 1, and 2.92. Since X = x — | the roots of the given equation are found by dimin- ishing these values by f = 0.67, which gives us the four roots of the given equation X = - 3.27, - 1.99, 0.33, 2.26. GRAPHIC SOLUTION OF EQUATIONS 105 15.11. Equivalent Sets of Simultaneous Equations. Two sets of simultaneous equations are equivalent if they have the same roots. It follows from what has been said that the two sets of curves corresponding to the two sets of equations must have the same intersection points. Thus by first adding and then subtracting the two equations (1) x^ + 3xy + y^ = 299, (2) x'^-3xy + y^ = -l, we obtain the equivalent set of equations (3) a;2 + 2/2 = 149, (4) xy = 50. The intersection points of the curves (1) and (2) must coin- cide with the intersection points of the curves (3) and (4).
What to read after A Short Course in College Mathematics, Comprising Thirty-Six Lessons On Algebra, Coordinate Methods, And Plane Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by Robert Douard Moritz to read online
To quickly assess the difficulty of the text, read a short excerpt:
Here A = 9,\, B = 216, hence iJ/(4 A) = 216/(4 x 81)= f. Substituting X = x — | in the above equation we obtain the new equa- tion 81 X* — 729 x2 - 162 X + 810 = 0, or, dividing through by 81, x< - 9 a;2 — 2x -1-10 = 0. The roots of this equation were found in 15.9 to be - 2.60, - 1.32, 1, and 2.92. Since X = x — | the roots of the given equation are found by dimin- ishing these values by f = 0.67, which gives us the four roots of the given equation X = - 3.27, - 1.99, 0.33, 2.26. GRAPHIC SOLUTION OF EQUATIONS 105 15.11. Equivalent Sets of Simultaneous Equations. Two sets of simultaneous equations are equivalent if they have the same roots. It follows from what has been said that the two sets of curves corresponding to the two sets of equations must have the same intersection points. Thus by first adding and then subtracting the two equations (1) x^ + 3xy + y^ = 299, (2) x'^-3xy + y^ = -l, we obtain the equivalent set of equations (3) a;2 + 2/2 = 149, (4) xy = 50. The intersection points of the curves (1) and (2) must coin- cide with the intersection points of the curves (3) and (4).
What to read after A Short Course in College Mathematics, Comprising Thirty-Six Lessons On Algebra, Coordinate Methods, And Plane Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by Robert Douard Moritz to read online
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