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The difference of two numbers is 5 and the difference of their reciprocals is1/20. Find the numbers. |
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Answer» Step-by-step explanation: LET the TWO NUMBERS be x and x - 5 . 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.
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