...Divide the number a into two such parts, that the sum of the squares of those parts shall be b. Ans. 11. It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14. 12. The sum of two numbers...

...of equations of the second degree. We give a few exampleS. 1. It is required to divide the number 14 into two such parts that the quotient of the greater...divided by the less, may be to the quotient of the less divided by the greater, as 16 to 9. Let x = the greater part; then 14 — x = the less, and by the...

...divide the number 40 into two such parts, that the sum of their squares shall be 818. Ans. 23 and 17. 3. It is required to divide the number 24 into two such parts, that their product shall be equal to 35 times their difference. Ans. 10 and 14. 2. To'find a number such,...

...from 10, and multiply the remainder by the number itself, the product shall be 21. " Ans. 7 or 3. 8. It is required to divide the number 24 into two such parts that their product shall be equal to 35 times their difference. Ans. 10 and 14. 9. Divide the number 346...

...horse worth three times the 1st : what were the values of the two horses. Ans. £6, and £9. Prob. 25. It is required to divide the number 24 into two such...be to the quotient of the less part divided by the jreater, as 4 to 1. Ans. 16 and 8. Prob. 26. A cistern is to be filled with water from three different...

...greater and 2x= the difference, then, &c. Ans. 18 and 14. 2. It is required to divide the number 14 into two such parts, that the quotient of the greater part divided by the less may b? to the quotient of the less divided by the greater as 48 to 27. Let x = the greater, then 14 —...

...Prob. 10. It is required to divide the number 14 into two such parts that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater as 16 to 9. Prob. 1 1 . What two numbers are as 5 to 4, the sum of whose cubes...

...•+«'+;/•• Prob. 7. Divide the number 49 into two such parts, that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater, as $ to £ . Ans. 21 and 28. Prob. 8. Divide the number a into two such parts,...

...horse worth three times the 1st : what were the values of the two horses. Ans. £6, and £9. Prob. 25. It is required to divide the number 24 into two such...divided by the greater, as 4 to 1. Ans. 16 and 8. Prob. 26. A cistern is to be filled with water from three different stop-cocks ; from the first it...

...whence, by the rule, x = 50 ± VT96"= 50 ± 14 ; hence, ж = 64, x — 36, and у = 36, у = 64. 11. It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Let x and у denote the parts. From the conditions...