Q84 of 134 Page 4


The sum of two natural numbers is 8. Determine the numbers, if the sum of theirreciprocals ishttps://static.philoid.co/ncertusercontent/solutions/user_files/63094/15042/images/extra-4_files/Image1295.gif .


Let one number be x.
Then the other number is 8 – x.



15 = x(8 - x)
15 = 8x - x 2
x 2 - 8x + 15 = 0
x 2 - 5x – 3x + 15 = 0
x(x – 5) – 3(x – 5) = 0
(x – 3)(x – 5) = 0
(x – 3) = 0 or (x – 5) = 0
x = 3 or x = 5
Therefore the numbers are 3 and 5.
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