Question

12. The sum of two natural numbers is 9 and the sum of their reciprocals is
Find the numbers.
​

Answer 1

Correct Question

• 12. The sum of two natural numbers is 72 and the sum of their reciprocals is 9

Find the numbers.

Answer

Given

• A word problem

• Sum of two natural no is 72

• And sum of their reciprocal is 9

To find

• The no

Solution

Let the no in tens place be x and no in ones place be y

According to the question

x+y = 72____(1)

While

$\tt\dfrac{1}{x}+\dfrac{1}{y}$

$\rightarrow\tt\dfrac{1}{x}+\dfrac{1}{y}$

$\rightarrow\tt\dfrac{x+y}{xy}$

$\rightarrow\tt\dfrac{x+y}{xy}=9$

=>72/xy = 9

=>72/xy = 9

=>xy = 8

Now

=>(x-y)²= (x+y)²-4xy

=>(x-y)²= (9)²-4×8

=>(x-y)² =81-32

=>x-y = √49

=>x-y = 7______(2)

Solving of Equation (1) and (2)

x+y = 72____(1)

x-y = 7______(2)

______

2x = 79

=>x = 39.5

Putting the value in Equation 1

x+y = 72

=>39.5+y =72

=>y = 72-39.5

=>y = 32.5

Hence the no is 32.5 and 39.5

Answer 2

Refers to attachment ♡~