The sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.

Answer

`12 and 14 `

Explanation

`x + y = 16 and (1)/(x) + (1)/(y) = (1)/(3) rArr (y+ x )/(xy ) = (1)/(3)rArr xy = 16 xx 3 = 48`.
` ( x- y) ^(2) = (x + y) ^(2) - 4xy = (16) ^(2) - (4 xx48) = 256 - 192 = 64 `
`rArr x - y = 8 or x - y = - 8` .
` therefore x - y = 8 or x - y = - 8`
`therefore (x + y =16, x - y =8) or (x + y =16, x - y = - 8)`