Question
Sun July 15, 2012 By:
 

the sum of two numbers is 8 & the sum of their reciprocals is 8/15. find the numbers

Expert Reply
Sun July 15, 2012

Let one number be X. The other number be Y.

GIVEN,

X+Y=8

X=8-Y ---------------(1)

1/X+1/Y=8/15

BY SIMPLIFING 1/X+1/Y=8/15 WE GET,

(X+Y)/XY=8/15

FROM (1) WE GET,

8/8Y-Y2=8/15

Y2-8Y+15=0

(Y - 3)(Y - 5) = 0

Y = 3 or 5

WE KNOW THAT X+Y=8

When Y=5, X=3

When Y = 3, X = 5
 
Thus, the two numbers are 3 and 5.
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