 | Thomas Simpson - Mathematics - 1792 - 292 pages
...get ^— = 360. Whence x comes out =« QUESTION LXXXIII. Tfiere are two Numbers, whofe Reflangle is equal to the Difference of their Squares ; and the Sum of their Squares is alfo equal to the Difference of their Cubes* fVhat are thoje Numbers ? Let x denote the lefier number,... | |
 | Peter Barlow - Mathematics - 1811 - 536 pages
...added to their product shall be a square. 1 9 40 9'9'T 7. To find two numbers, whose difference is equal to the difference of their squares, and the sum of their squares a square. C 4 3 v I -, -, or any two fractions the L sum of which is unity. 8. To find two such numbers,... | |
 | John Bonnycastle - Algebra - 1813 - 456 pages
...them : how many sheep did he buy ? Ans. 7¿> 14. It is required to find two numbers, such that their product shall be equal to the difference of their...their squares equal to the difference of their cubes. Ans. |V5 and ^(5 + -v'5) 15. The difference of two numbers is 8, and the difference of their fourth... | |
 | John Bonnycastle - Algebra - 1818 - 326 pages
...quadratic equation. Ans. 1 ± ^/(2^/34 — 11) 23. It is required to find two numbers such, that their product shall be equal to the difference of their...their squares equal to the difference of their cubes. Ans. \b and 24. The arithmetical mean of two numbers exceeds the geometrical mean by 13, and the geometrical... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...them : how many sheep did he buy ? Ans. 75 14. It is required to find two numbers, such that their product shall be equal to the difference of their...their squares equal to the difference of their cubes. Ans. \^/ 5 and KS-J-^/O) 15. The difference of two numbers is 8, and the difference of their fourth... | |
 | John Radford Young - Algebra - 1832 - 408 pages
...negative : it is therefore inadmissible. QUESTION VIII. To find two numbers, such, that their product may be equal to the difference of their squares, and the...their squares equal to the difference of their cubes. If we assume ax and (a + 1)ж for the numbers, a being = I + ii/ 5, we shall fulfil the first condition... | |
 | John Hind - Algebra - 1837 - 584 pages
...to one another. Answer : 1 (3 + \/5), and i (l + \/5). 7. There are two magnitudes whose product is equal to the difference of their squares, and the sum of their squares is also equal to the difference of their cubes ; find them. Answer : 1 \/5, and ^ (5 + \/5). 8. Required... | |
 | John Radford Young - Algebra - 1838 - 368 pages
...What are the numbers ? Ans. 4, 12, and 36. 12. It is required to find two numbers, such, that their product shall be equal to the difference of their...their squares equal to the difference of their cubes. 5 + V 5 V5 Ans. , and — -. 13. The product of five numbers in arithmetical progression is 10395,... | |
 | John Radford Young - 1839 - 332 pages
..."What are the numbers? Ans. 4, 12, and 36. 12. It is required to find two numbers, such, that their product shall be equal to the difference of their...their squares equal to the difference of their cubes. 5 4- \/ 5 л/5 Ans. — '-— — , and -— . "^ 13. The product of five numbers in arithmetical progression... | |
 | John D. Williams - Algebra - 1840 - 634 pages
...sheep, and -^^=16 dollars, the price each cost. 24. It is required to find two numbers, such that their product shall be equal to the difference of their squares, and the sum of their squares equal to their cubes. Let x= less number, and xy the greater ; then xy^x=x^if— z3, and z'y'-\-x*=3?y3=x3,... | |
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Find two numbers whose product is equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes. 
