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The sum of a non-zero number and 4 times its reciprocal is 17/2. What is the number?
- A8
- B12
- C16
- D4
Answer not set
Discussion 1
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CCommunity
Let the number be ‘x’
⇒ x + 4/x = 17/2
⇒ 2x2 + 8 = 17x
⇒ 2x2 – 17x + 8 = 0
⇒ 2x2 – 16x – x + 8 = 0
⇒ 2x(x – 8) – 1(x – 8) = 0
⇒ (x – 8)(2x – 1) = 0
⇒ x = 8, 1/2
∴ The number is 8
⇒ x + 4/x = 17/2
⇒ 2x2 + 8 = 17x
⇒ 2x2 – 17x + 8 = 0
⇒ 2x2 – 16x – x + 8 = 0
⇒ 2x(x – 8) – 1(x – 8) = 0
⇒ (x – 8)(2x – 1) = 0
⇒ x = 8, 1/2
∴ The number is 8