Answer:
number is 5
Step-by-step explanation:
The reciprocal of a number n is [tex]\frac{1}{n}[/tex] , thus
n - [tex]\frac{1}{n}[/tex] = [tex]\frac{24}{5}[/tex]
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 = - [tex]\frac{1}{5}[/tex]
However, n > 1 , thus n = 5
That is the number is 5
