Question

if the difference between a number and its reciprocal is 24/5 find its number. ​ A.5. B.10. C.15 D.20

Answer 1

Answer :

option (A) 5

Step-by-step explanation :

Let the number be x

It's reciprocal = 1/x

Given,

the difference between a number and its reciprocal is 24/5

  $\bf x-\frac{1}{x} = \frac{24}{5} \\\\ \frac{x^2-1}{x} =\frac{24}{5} \\\\ 5(x^2-1)=24(x) \\\\ 5x^2-5=24x \\\\ 5x^2-24x-5=0 \\\\ 5x^2+x-25x-5=0 \\\\ x(5x+1) -5(5x+1)=0 \\\\ (5x+1)(x-5)=0 \\\\ \longrightarrow 5x+1=0 \ ; \ x=-1/5 \\\\ \longrightarrow x-5 =0 \ ; x=+5$

The number is 5 (or) -1/5

Verification :

• The number = 5
• It's reciprocal = 1/5

Difference = 24/5

 $5-\frac{1}{5}=\frac{24}{5} \\\\ \frac{5 \times 5}{5} -\frac{1}{5}=\frac{24}{5} \\\\ \frac{25}{5} -\frac{1}{5} =\frac{24}{5} \\\\ \frac{25-1}{5} =\frac{24}{5} \\\\ \frac{24}{5} =\frac{24}{5}$

Hence verified!