Question

If the difference between the number and it's recipoical is 24/5. Find the number. Please send me explaination
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Answer 1

Answer:

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Step-by-step explanation:

number is either 5 or -1/5

let required number is x .

a/c to question,

number - reciprocal of number = 24/5

⇒x - 1/x = 24/5

⇒x² - 1 = 24x/5

⇒5x² - 5 = 24x

⇒5x² - 24x - 5 = 0

⇒5x² - 25x + x - 5 = 0

⇒5x(x - 5) +1(x - 5) = 0

⇒(5x + 1)(x - 5) = 0

⇒x =5, -1/5

Answer 2

Given:

The difference the number and its reciprocal is 24/5.

To Find:

The number.

Solution:

Define x:

$\text{Let the number = x}$

$\text{The reciprocal = }\dfrac{1}{x}$

Solve x:

$\text{The difference is }\dfrac{24}{5}$

$x - \dfrac{1}{x} = \dfrac{24}{5}$

$\dfrac{x^2 - 1}{x} = \dfrac{24}{5}$

$5(x^2 - 1) = 24x$

$5x^2 - 5 = 24x$

$5x^2 - 24x- 5 = 0$

$(x - 5) (5x + 1) = 0$

$x = 5 \text{ or } x= -\dfrac{1}{5} \text{(Rejected, assumed positive)}$

Find the numbers:

$\text{Number }= x$

$\text{Number }= 5$

$\text{Reciprocal }= \dfrac{1}{x}$

$\text{Reciprocal }= \dfrac{1}{5}$

Answer: The number is 5 and 1/5