 The sum of three numbers in arithmetical progression is 15; and the sum of the squares of the two extremes is 58. What are the numbers'?  A School Algebra - Page 435by George Albert Wentworth - 1894 - 362 pagesFull view - About this book
 | Jeremiah Day - Algebra - 1820 - 352 pages
...equations, we have a; = 12, and y=4. The numbers required, therefore, are 8, 1 2, 1 6, and 20. Prob. 2. The sum of three numbers in arithmetical progression is 9, and the sum of their cubes is 1 53. What are the numbers ? Ans. 1 , 3, and 5. ^ Prob. 3- The sum of three numbers in arithmetical... | |
 | Jeremiah Day - Algebra - 1827 - 352 pages
...equations, we have o:=12, and y=4. The numbers required, therefore, are 8, 12, 16, and 20. Prob. 2. The sum of three numbers in arithmetical progression is 9, and the sum of their cubes is 1 53. What are the numbers ? Ans. 1, 3, and 5. Prob. 3. The sum of three numbers in arithmetical... | |
 | Horatio Nelson Robinson - Algebra - 1844 - 184 pages
...problem.. We take, x— 3y=lst.~ 3r2=4 Therefore, x — %=8. y= 2 a; — y=12, &c., the answer. 2. The sum of three numbers in arithmetical progression is 9, and the sum of their cubes is 153. What are the numbers. (x— y)+(a;)+(z+y), or 3z=9, or z=3. And a^ — 3x*y-\-3xy* —... | |
 | James Bates Thomson - Algebra - 1844 - 272 pages
...equations, we have £=12, and y=4. The numbers required, therefore, are 8, 12, 16 and 20. Prob. 25. The sum of three numbers in arithmetical progression is 9, and the sum of their cubes is 153. What are the numbers ? • Prob. 26. The sum of three numbers in arithmetical progression... | |
 | Jeremiah Day - Algebra - 1847 - 358 pages
...equations, we have x=lZ, and y=4. The numbers required, therefore, are 8, 12, 16, and 20. Prob. 2. The sum of three numbers in arithmetical progression is 9, and the sum of their cubes is 153. What are the numbers ? . Ans. 1, 3, and 5. Prob. 3. The sum of three numbers in arithmetical... | |
 | Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...equations, we have z=12, and y=4. The numbers required, therefore, are 8, 12, 16 and 20. Prob. 25. The sum of three numbers in arithmetical progression is 9, and the sum of their cubes is 153. What are the numbers ? Prob. 26. The sum of three numbers in arithmetical progression... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...though satisfying the algebraical conditions, being excluded from the nature of the question. 3. The snm of three numbers in arithmetical progression is 9, and the sum of their cubes 153. What arc the numbers ? Let * — y, a-, x + y represent the numbers ; then x — y + .r... | |
 | Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1874 - 322 pages
...added to the square of the second, shall equal the second part added to thelsquare of the first ? 2- The sum of three numbers in arithmetical progression is 9, and the sum of their reciprocals is f J; find the numbers. 3. Given 2x\/ l — j.—z'—x + l, to find a;. 4. A ladder... | |
 | George Albert Wentworth - Algebra - 1889 - 540 pages
...27. The sum of three numbers in arithmetical progression is 33, and the sum of their squares is 461. Find the numbers. Let a — d, a, a + d be the three numbers. Then a — d + a + a + d = 33 (1) (a _ rf)a + a2 + (a + d)2 = 461 (2) From (1), 3a=33 а = 11 (3) From (2),... | |
 | George Albert Wentworth - Algebra - 1892 - 538 pages
...6. If 1, 2, 5 be added to the numbers, the three resulting numbers are in geometrical progression. Find the numbers. Let a — d, a, a + d be the three numbers. Then 3a = 6 (1) a + 2 _ g + rf + 5 ,2) a_d+l a+2 Prom (1), a = 2 Substitute value of a in (2), 4 =7 + d 3-rf~... | |
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