 | Mathematics - 1801 - 446 pages
...numbers are 3, 7, 11 and 15. 8. To ALGEBRA. 8. To find three numbers in geometrical progression,' whose sum shall be 14, and the sum of their squares 84. Let x, y and z be the numbers sought ; Then «zzzry1 by the nature of proportion, . And But ,Y-|-z — 14... | |
 | Samuel Webber - Mathematics - 1808 - 466 pages
...6=3, And the numbers are 3, 7, 11, and 15. 8. To find three numbers in geometrical progression^ whose sum shall be 14, and the sum of their squares 84. Let > , !/, and z be the numbers sought ; Then xz—y* by the nature of proportion, And •! r. ^ ,z,~... | |
 | John Bonnycastle - Algebra - 1811 - 230 pages
...6=3, and the numbers are 3, 7, 11, and 15. 8. To find three numbers in geometrical progression, whose sum shall be 14, and the sum of their squares 84. Let x, y, and z be the numbers sought; Then ^z=i/2, by the nature of proportion, the But x+z= 14 — y, by... | |
 | John Bonnycastle - Algebra - 1813 - 456 pages
...rule, Whence the numbers are 3, 7, 11, and 15. 8. Itisrequired to find three numbers in geqmetrir cal progression^, such that their sum shall be 14, and the sum of their squares 84. Let x, y, and % be the three numbers, Then xz =уг, by the nature of proportion, And And x* + 2zx + z* =... | |
 | John Bonnycastle - Algebra - 1818 - 284 pages
...consequently z= — 6+ ^/ (36 + 45) = — 6+9=3, by the rule, Whence the numbers are 3, 7, 11, and 15. 8. It is required to find three numbers in geometrical...shall be 14, and the sum of their squares 84. Let x, y, and z be the three numbers, Then xz=y3, by the nature of proportion, y the question, Hence a:+2... | |
 | John Bonnycastle - Algebra - 1818 - 326 pages
...consequently x= — 6+ ^/ (36 + 45) = — 6+9=3, by the rule, Whence the numbers are 3, 7, 11, and 15. 8. It is required to find three numbers in geometrical...shall be 14, and the sum of their squares 84. Let z, y, and z be the three numbers, Then z2=y3, by the nature of proportion, And ^!|I^L84 \ by the Cation,... | |
 | Jeremiah Day - Algebra - 1820 - 352 pages
...geometrical progression, may be solved, as in other parts of algebra, by the reduction of equations. Prob. 1. Find three numbers in geometrical progression, such...shall be 14, and the sum of their squares 84. Let the three numbers be x, y, and z. By the conditions, x:y::y:z, or xz=y 3 And x+y+z=l4 And * a +y2+z*=84... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...consequently i= 6 + ^(36-4-45)= — 6+9=3, by the rule. Whence the numbers are 3, 7, 11, and 15. 8. It is required to find three numbers in geometrical progression, such that their sum shall be 14, anil the sum of their squares 84. Let x, y. and z he the three numbers, Then xz—y 3 , by the nature... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...-аг" 3|0_3(Э'°— а") »(Д9049— 1024) *- r— I ~ 1— г ~~ _2 "~ 3le " ~ 59049 " 59049 3. Find three numbers in geometrical progression, such, that their sum shall be equal to 7, and the gum of their squares to 21. Let the numbers be «»y, and z; then by question And... | |
 | Jeremiah Day - Algebra - 1827 - 352 pages
...geometrical progression, may be solved, as in other parts of algebra, by the reduction of equations. Prob.l. Find three numbers in geometrical progression, such...shall be 14, and the sum of their squares 84* Let the three numbers be x, y and z. By the conditions x : y. '.y : z, or xz=y3 i And x+y+z = l4> And x*+y"-... | |
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It is required to find three numbers in geometrical progression, such that their sum shall be 14, and the sum of their squares 84. Ans. 2, 4, and 8. 8. There are four numbers in geometrical progression... 
