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in Polynomials by (31.2k points)
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If 12 is added to a natural number, then it becomes 160 times of its reciprocal. Find that number.

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Best answer

Let x be a natural number.

According to the question, when 12 is added to a natural number.

It becomes 160 times its reciprocal

x + 12 = 160 × 1/x

⇒ x2 + 12x = 160

⇒ x2 + 12x – 160 = 0

⇒ x2 + (20 – 8) x – 160 = 0

⇒ x2 + 20x – 8x – 160 = 0

⇒ x (x + 20) – 8 (x + 20) = 0

⇒ (x + 20) (x – 8) = 0

if x + 20 = 0, then x = -20

or x – 8 = 0, then x = 8

x is a natural number, 

so it cannot be negative

x = 8

Hence, number is 8.

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