...Also 12 + 8 x 10 + 5= 300. 16 x 7,5 = 120 16 + 8 x 7,5 + 5 = 300. PROBLEM L. , Tofind two numbers, so that their sum, their product, and the difference of their squares, may be all equal to one another. The greater being denoted by x, and the lesser by y, we have x + y = xy, and x + y = x* — y2 : the...

...found, if the two unknown quantities were represented by x and y respectively. Problem 1. Required two numbers, such, that their sum, their product,...the difference of their squares, may be all equal. Let af-ry=the greater; and x—y= the lesser; , lhe and 2x=( From the 2d equation y=% ; .*. y"—\...

...found, if (he two unknown quantities were represented by x and y respectively. Problem 1. Required two numbers, such, that their sum, their product,...the difference of their squares, may be all equal. Let z-fys=the greater; and x— y— the lesser; . the and 2x= From the 2d equation, y=| ; .*. ya—\...

...ANS. ^i ± v/i' Ex. 11. Find the values of*, in the equation x*— 12 x* + 16=0? ANS. Ex. 12. Required two numbers, such that their sum, their product, and...the difference of their squares, may be all equal ? ANS. < and Ex. 13. Required two numbers, such, that their sum, their product, and the sum of their...

...given p, and also the product F, of the sums when each is increased by a given number (a and 6). 14. To find two numbers such, that their sum, their product, and the difference of their squares, shall be all equal. , Ans. x=. 15. Given the sum a, of two numbers, and the sum of their square roots...

...of two numbers is 7, and the sum of their 5th powers 3157. Required the numbers. Ans. 5 and 2. 16. Find two numbers, such that their sum, their product, and the difference of their squares, may all be equal to one another. Ans. ^ ± J V5, and f ± \ V5. 17. Divide the number 100 into two such...

...same, because the equations (A) and (B) are symmetrical with respect to as and y. [See art. 112.] 214. Find two numbers such that their sum, their product, and the difference of their squares, shall be all equal. As before, let the one be a; anil the other y. Their sum is x + y, their product...

...the quotient will be 2; but, if 27 be added to the number, the digits will be inverted 1 Jlns. 36. 9. Find two numbers such that their sum, their product, and the difference of their squares may all be equal to one anothe r. Jlns, £ ± £ v/ 5, and f ± £ v/ 5. 10. A and B hired a pasture, into...

...given p, and also the product P, of the sums when each is increased by a given number (a and b}. 14. To find two numbers such, that their sum, their product, and the difference of their squares, shall be all equal. , 1+J5 , 3.HJ5 Ans. y = .=yL., anda; = — v . 15. Given the sum a, of two numbers,...

...product of the two numbers thus obtained shall be d ? ,-<*«, where / = — — — — 6. cc 9. To find two numbers, such that their sum, their product...of their squares may be all equal to one another. Ans. -+v/-and -'+ V —. 1 0. Divide the number 100 into two such parts, that their product and the...