Find the numbers.
The sum of two numbers is 8 and the sum of their
reciprocals is 8/15. Find the numbers.
Answers
Answered by
1
Answer:
3 and 5
Step-by-step explanation:
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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