The sum of a number and its reciprocal is 24/15. Find the number.
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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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no
Step-by-step explanation:
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