Question 103791: The sum of two numbers is 28, and their product is 7. Find the sum of the reciprocals of the numbers. Found 2 solutions by ursuchacrass, htmentor:Answer by ursuchacrass(5) (Show Source):
You can put this solution on YOUR website! x and y are two numbers
x+y=28.....eqn 1
xy=7.......eqn 2
from eqn 2
y=7x
substitute to eqn 1
x+7x=28
8x=28......divide both sides by 8
x=7/2
subst5itute the equivalent of x to eqn 1 to get the value of y\]
7/2+y=28
y=28-7/2
y=49/2
You can put this solution on YOUR website! x+y = 28 (1)
x*y = 7 (2)
Note that it is not necessary to solve for x and y, since what is asked for is the sum of the reciprocals.
Easiest way: Divide eqn (1) by eqn (2)
(x+y)/(x*y) = 4
Or x/(x*y) + y/(x*y) = 4 which reduces to 1/y + 1/x = 4
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