Q1 of 227 Page 107

The sum of a number and its reciprocal is . Find the number.

Let x be the required number. Then, the reciprocal is .


⇒ sum of a number and its reciprocal is


⇒


⇒


⇒ 8(x2 + 1) = 65x


⇒ 8x2 + 8 = 65x


⇒ 8x2 – 65x + 8 = 0


⇒ 8x2 – x – 64x + 8 = 0


⇒ x(8x – 1) – 8(8x – 1) = 0


⇒ (x – 8) (8x – 1) = 0


x – 8 = 0 or 8x – 1 = 0


x = 8 or 8x = 1



Therefore, the two required numbers are 8 and .


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