Question

if the difference between a number and its reciprocal is 24/5 find its number. ​

Answer 1

Step-by-step explanation:

let the number be 'a'

then, according to the question,

a-1/a=24/5

a^2-1=(24/5)a

5(a^2-1)=24a

5a^2+24a-5=0

5a^2+25a-a-5=0.

5a(a+5)-1(a+5)=0.

(5a-1)(a+5)=0.

5a-1=0,a=1/5

or, a+5=0,a=-5.

but only a=1/5 satisfies the condition, so

answer is a=1/5.

Answer 2

The number is 5 or $-\dfrac{1}{5}$

Step-by-step explanation:

Let the number be x.

The reciprocal of x is $\dfrac{1}{x}$

Difference between number (x) and reciprocal is $\dfrac{24}{5}$

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

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

$5x^2-5=24x$

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

$5x^2-25x+x-5=0$

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

So, x = 5 ,$-\dfrac{1}{5}$

Hence, the number is 5

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