The difference between two positive numbers x and y (x y) is 4 and the difference between their reciprocal is . Find the numbers.

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KnowledgeBoat · Accepted Answer

Given, ⇒ x y Difference between two positive numbers x and y (x y) is 4. ∴ x - y = 4 ⇒ x = y + 4 ........(1) Difference between their reciprocal is . Substituting value of x from equation (1) in (2), we get : ⇒ 21(y + 4) - 21y - 4y(y + 4) = 0 ⇒ 21y + 84 - 21y - 4y² - 16y = 0 ⇒ 4y² + 16y - 84 = 0 ⇒ 4(y² + 4y - 21) = 0 ⇒ y² + 7y - 3y - 21 = 0 ⇒ y(y + 7) - 3(y + 7) = 0 ⇒ (y - 3)(y + 7) = 0 ⇒ y - 3 = 0 or y + 7 = 0 ⇒ y = 3 or y = -7. Since, numbers are positive. ∴ y = 3. ⇒ x = y + 4 = 3 + 4 = 7. Hence, numbers are 3 and 7.

Mathematics

The difference between two positive numbers x and y (x y) is 4 and the difference between their reciprocal is . Find the numbers.

Linear Equations

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