Question

If the difference and product of two numbers are 5 and 36 respectively, then find the difference of their reciprocals

Answer 1

first we take the l. c. m. of 5 and 36

we get 210

The difference = 1/5 - 1/36 = 42 - 5 / 210

= 37/210 .

The product is 1/5*1/36= 1/210 .

the ans of difference is 37/210 and the ans of product is 1/210

I hope it will help you, thanks

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The difference between the reciprocals is }}}\dfrac{5}{36}.$

Step-by-step explanation:

Let the given two numbers be represented by x and y respectively, where x is greater than y.

So, according to  the given information, we have

$x-y=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\xy=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Dividing equation (i) by (ii), we get

$\dfrac{x-y}{xy}=\dfrac{5}{36}\\\\\\\Rightarrow \dfrac{x}{xy}-\dfrac{y}{xy}=\dfrac{5}{36}\\\\\\\Rightarrow \dfrac{1}{y}-\dfrac{1}{x}=\dfrac{5}{36}.$

Thus, the required difference between the reciprocals of the two numbers is $\dfrac{5}{36}.$