Key to Davies' Bourdon, With Many Additional Examples, Illustrating the Algebraic Analysis; Also, a Solution of All the Difficult Examples in Davies' Legendre
Key to Davies' Bourdon, With Many Additional Examples, Illustrating the Algebraic Analysis; Also, a Solution of All the Difficult Examples in Davies' Legendre
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In our eReader you can find the full English version of the book. Read Key to Davies' Bourdon, With Many Additional Examples, Illustrating the Algebraic Analysis; Also, a Solution of All the Difficult Examples in Davies' Legendre 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 Key to Davies' Bourdon, With Many Additional Examples, Illustrating the Algebraic Analysis; Also, a Solution of All the Difficult Examples in Davies' Legendre
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To quickly assess the difficulty of the text, read a short excerpt:
a;2 - y^ + ar - y = 150 • • ' • (1), x^ + y^ + x + y = SSO • • • (2); adding member to member, and reducing, x^ + x = 240; whence, x=-^± ^^40 + 1 = - - =b y ; or, considering only the positive solution, a; = 15; whence, from (1), by substitution, y = 9.
8. There are two numbers whose difference is 15, and half their product is equal to the cube of the lesser number : what are the numbers ?
Let X and y denote the numbers.
From the conditions of the problem, a; — y = 15 • • • ♦ (1), |^ = y3, or ^... = 2y2 . . . (2); substituting in (1) and dividing both members by 2, whence, ^ 2"" 2 ' 1 /15 , 1 1 11 2^ = 4^V-2+l6 = 4=^T^ considering only the positive solution, y = 3 ; whence, from (1), ar = 18.
182.] EQUATIONS OF THE SECOND DEGREE. 91 9. What two numbers are those whose sum multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12?
Let X and y denote the numbers.
From the conditions, ' (x + y) xz= 77, or x^ + xy-=n . • • (1) ; (a:-y)y=12, or ary - y2 = 12 • • • (2); make x z=py; whence, {p^+p)y^ = 17, or, y*=^5^ • • • (3), 12 {p -l)y» = 12, or, y^=j^ry • • • (4); equating the second members and reducing, 2 65 77 ^ -I2^=-12' 65 / 77 , 4225 65 23 whence, ^ = - ± y'- _ + -^ = _ ± _; taking the upper sign, _88__ 11 -^ "" 24 "■ 3 9 /0£t Q substituting in (4), y = V "q" = 2 '^' whence, ^ = "o" V^j 42 21 taking the lower sign, -^ — 24 ~ l2 ' 92 KEY TO DAVIE8* BOURDON.
What to read after Key to Davies' Bourdon, With Many Additional Examples, Illustrating the Algebraic Analysis; Also, a Solution of All the Difficult Examples in Davies' Legendre?
You can find similar books in the "Read Also" column, or choose other free books by Charles Davies to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
a;2 - y^ + ar - y = 150 • • ' • (1), x^ + y^ + x + y = SSO • • • (2); adding member to member, and reducing, x^ + x = 240; whence, x=-^± ^^40 + 1 = - - =b y ; or, considering only the positive solution, a; = 15; whence, from (1), by substitution, y = 9.
8. There are two numbers whose difference is 15, and half their product is equal to the cube of the lesser number : what are the numbers ?
Let X and y denote the numbers.
From the conditions of the problem, a; — y = 15 • • • ♦ (1), |^ = y3, or ^... = 2y2 . . . (2); substituting in (1) and dividing both members by 2, whence, ^ 2"" 2 ' 1 /15 , 1 1 11 2^ = 4^V-2+l6 = 4=^T^ considering only the positive solution, y = 3 ; whence, from (1), ar = 18.
182.] EQUATIONS OF THE SECOND DEGREE. 91 9. What two numbers are those whose sum multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12?
Let X and y denote the numbers.
From the conditions, ' (x + y) xz= 77, or x^ + xy-=n . • • (1) ; (a:-y)y=12, or ary - y2 = 12 • • • (2); make x z=py; whence, {p^+p)y^ = 17, or, y*=^5^ • • • (3), 12 {p -l)y» = 12, or, y^=j^ry • • • (4); equating the second members and reducing, 2 65 77 ^ -I2^=-12' 65 / 77 , 4225 65 23 whence, ^ = - ± y'- _ + -^ = _ ± _; taking the upper sign, _88__ 11 -^ "" 24 "■ 3 9 /0£t Q substituting in (4), y = V "q" = 2 '^' whence, ^ = "o" V^j 42 21 taking the lower sign, -^ — 24 ~ l2 ' 92 KEY TO DAVIE8* BOURDON.
What to read after Key to Davies' Bourdon, With Many Additional Examples, Illustrating the Algebraic Analysis; Also, a Solution of All the Difficult Examples in Davies' Legendre?
You can find similar books in the "Read Also" column, or choose other free books by Charles Davies to read onlineMoreLess
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