if the difference between two numbers is 5 and their reciprocal is 1/10 . find the numbers
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According to the question.
⇒ x(x-5) = 50
⇒ x2 - 5x - 50 = 0
⇒ x2 - 10x + 5x - 50 = 0
⇒ x (x - 10) + 5 (x - 10) = 0
⇒ (x+5) (x-10) = 0
⇒ (x+5) (x-10) = 0
⇒ x = -5 or 10
⇒ x = 10 (x = -5 , rejected)
∴ Two numbers are 10 and (10-5) = 5