The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.

Let the numbers be ‘a’ and ‘b’.


Given, sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8.


a + b = 8


a = 8 – b


Also, 15 × (1/a + 1/b) = 8


1/a + 1/b = 8/15


1/a + 1/(8 – a) = 8/15


15(8 – a + a) = 8(8a – a2)


a2 – 8a + 15 = 0


a2 -5a – 3a + 15 = 0


a(a – 5) -3(a – 5) = 0


(a – 3)(a – 5) = 0


a = 3, 5


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