The sum of a natural number and its reciprocal is 65/8. Find the natural number.

Question

KnowledgeBoat · Accepted Answer

Let the numbers be x and its reciprocal be . Given, Sum of natural number and it's reciprocal = ⇒ x + ⇒ ⇒ 8 × (x2 + 1) = 65x ⇒ 8x2 + 8 - 65x = 0 ⇒ 8x2 - 64x -x + 8 = 0 ⇒ 8x(x - 8) - 1(x - 8) = 0 ⇒ (8x - 1)(x - 8)= 0 ⇒ (8x - 1) = 0 or (x - 8) = 0 [Using zero-product rule] ⇒ 8x = 1 or x = 8 ⇒ x = or x = 8. Hence, the natural number is 8.

Mathematics

The sum of a natural number and its reciprocal is 65/8. Find the natural number.

Quadratic Equations

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