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