Question

The sum of two numbers is 50 and their product is 75. What is the sum of the reciprocals of these numbers ?​

Answer 1

Answer:

The sum of the reciprocals of these numbers is (2/3)

Step-by-step explanation:

let two numbers are X and Y.

Given

X + Y = 50 ----(1)

XY = 75------ (2)

by (1)/(2) we get

(X + Y)/XY = 50/75

=> 1/Y + 1/X = 2/3

So , we get the sum of reciprocals of these numbers is 2/3

Answer 2

Given,

Sum of two numbers $\[ = 50\]$

Product of two numbers $\[ = 75\]$

Solution,

Consider the two numbers are x and y.

$\[\begin{array}{l}x + y = 50 - - - - \left( 1 \right)\\xy = 75 - - - - - \left( 2 \right)\end{array}\]$

Calculate the sum of reciprocal of these numbers,

$\[ = \frac{1}{x} + \frac{1}{y}\]$

$\[ = \frac{{x + y}}{{xy}}\]$

$\[ = \frac{{50}}{{75}}\]$

$\[ = \frac{2}{3}\]$

Hence the sum of the reciprocals of these numbers is $\[\frac{2}{3}\]$.