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If the difference between a number and its reciprocal is 24/5, find the number. |
Answer» Let a number be x. Its reciprocal is 1/x x - 1/x = 24/5 (x2 - 1)/x = 24/5 5x2 – 5 - 24x = 0 ⇒ 5x2 – 24x – 5 = 0 5x2 – 25x + x – 5 = 0 5x(x – 5) + 1 (x – 5) = 0 (5x + 1)(x – 5) = 0 x = -1/5, 5 ∴ The number is -1/5 or 5. |
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