. If the difference between a number and its reciprocal is 24/5, find the number.

number is 5

Step-by-step explanation:

The reciprocal of a number n is , thus

n - =

Multiply through by 5n to clear the fractions

5n² - 5 = 24n ( subtract 24n from both sides )

5n² - 24n - 5 = 0 ← in standard form

(n - 5)(5n + 1) = 0 ← in factored form

Equate each factor to zero and solve for n

n - 5 = 0 ⇒ n = 5

5n + 1 = 0 ⇒ 5n = - 1 ⇒ n = -

However, n > 1 , thus n = 5

That is the number is 5

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