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A number is greater than twice its reciprocal by 31/4. Find the number.
- A7
- B8
- C9
- D6
Answer not set
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CCommunity
Let the number be ‘x’.
A number is greater than twice its reciprocal by 31/4.
⇒ x = 2(1/x) + 31/4
⇒ x - 2/x = 31/4
⇒ 4(x2 - 2) = 31x
⇒ 4x2 - 31x - 8 = 0
⇒ 4x2 - 32x + x - 8 = 0
⇒ 4x(x - 8) + 1(x - 8) = 0
⇒ (x - 8)(4x + 1) = 0
x = 8 or x = - 1/4
∴ x = 8
A number is greater than twice its reciprocal by 31/4.
⇒ x = 2(1/x) + 31/4
⇒ x - 2/x = 31/4
⇒ 4(x2 - 2) = 31x
⇒ 4x2 - 31x - 8 = 0
⇒ 4x2 - 32x + x - 8 = 0
⇒ 4x(x - 8) + 1(x - 8) = 0
⇒ (x - 8)(4x + 1) = 0
x = 8 or x = - 1/4
∴ x = 8