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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. "
Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ... - Page 252
by Jeremiah Day, James Bates Thomson - 1844 - 252 pages
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A treatise on algebra, in practice and theory: with notes and illustrations ...

Algebra - 1813
...rale, Whence the numbers are 3, ", 11, and 15. 8. Itisrequired to find three numbers in geometrir cal progression^, such that their sum shall be 14, and the sum of their squares 84. Let x, y, and z be the three numbers, Then xz=y*, by the nature of proportion, ,, the Hence x + z=...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 260 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...sum shall be 14, and the sum of their squares 84. Let x, y, and z be the three numbers, Then xx=y3 , by the nature of proportion, y the question, . Hence...
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An introduction to algebra: being the first part of a course of mathematics ...

Jeremiah Day - Algebra - 1820 - 332 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...sum 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 And x+y+z=l4 And *a+y2+z*=84...
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An introduction to algebra: with notes and observations, designed for the ...

John Bonnycastle, James Ryan - Algebra - 1825 - 312 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 xzy3, by the nature...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 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...
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An introduction to algebra: being the first part of a Course of mathematics ...

Jeremiah Day - Algebra - 1827 - 332 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...sum 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...
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A concise system of mathematics

Alexander Ingram - 1830
...third, and so on. In what time will he overtake the first ? oix _ i -^ * = (*+7)9. Ans. 18 days. 7- To find three numbers in geometrical progression, such, that their sum shall be , . and the sum of their squares 21. Liet x, y, 2, be the numbers. xz=y*, x+y + z = J, aa+y* + z* =21....
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An Introduction to Algebra ...

Jeremiah Day - 1832
...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 that their sum shall be 14, and the sum of thensquares 84. Let the three numbers be x, y, and z. By the conditions, x :y : :y : z, or xz=yl And...
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An introduction to algebra. To which is added an appendix containing a ...

John Bonnycastle, Samuel Maynard - 1836
...numbers are 3, 7, 11, and 15. 8. It is required to find three numbers iu geometrical progression, Mich that their sum shall be 14, and the sum of their squares 84. Let x, y, and z, be the three numbers, then xzy1, by the nature of the progression. y the hence...
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An Elementary Treatise on Algebra, Theoretical and Practical: With Attempts ...

John Radford Young - 1839
... 4, or 10 : hence the three numbers are 5, 9, and 19 ; or rather 19, 9, and 5. QUESTION II. It is required to find three numbers in geometrical...sum shall be 14, and the sum of their squares 84. Let -, x, and xy, be the three numbers ; У then, by the question, - + x + xy = 14, У .-. from the...
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