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The sum of a non-zero number and twice its reciprocal is 33/4. Find the number.
- A9
- B10
- C11
- D8
Answer not set
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CCommunity
Let the non zero number be x and its reciprocal be 1/x
From the given data sum of the non – zero number and twice its reciprocal is 33/4
⇒ x + 2/x = 33/4
⇒ x2 + 2 = 33x/4
⇒ 4x2 + 8 = 33x
⇒ 4x2 - 33x + 8 = 0
⇒ 4x2 - 32x - x + 8 = 0
⇒ 4x(x - 8) - 1(x - 8) = 0
⇒ (4x – 1)(x - 8) = 0
∴ x = ¼ and x = 8
From the given data sum of the non – zero number and twice its reciprocal is 33/4
⇒ x + 2/x = 33/4
⇒ x2 + 2 = 33x/4
⇒ 4x2 + 8 = 33x
⇒ 4x2 - 33x + 8 = 0
⇒ 4x2 - 32x - x + 8 = 0
⇒ 4x(x - 8) - 1(x - 8) = 0
⇒ (4x – 1)(x - 8) = 0
∴ x = ¼ and x = 8