Question

Q1.The Sum of two natural numbers is 9 and the sum of their reciprocals is 9/20 find the numbers​?

Answer 1

Explanation:

Given

Sum of two natural numbers is 9

sum of their reciprocals is 9/20

To find

We have to find the numbers

$\sf\huge\bold{\underline{\underline{{Solution}}}} </p><p>Solution</p><p>$

Let the first number be 'x'

Second number be 'y'

According to the question:

➙x+y= 9

x= 9-y―――❶

Sum of their reciprocals is 9/20

Reciprocals of numbers be 1/x & 1/y respectively.

➙1/x+1/y= 9/20

from equation 1

➙1/9-y+1/y= 9/20

➙y+9-y/y(9-y)= 9/20

➙9/9y-y²=9/20

since 9 lies on both sides on the numerator so,it gets cancelled

➙20×1= 9y-y²

➙20-9y+y²

➙y²-9y+20

➙y²-5y-4y+20

➙y(y-5)-4(y-5)

➙(y-4)(y-5)=0

➙y-4=0 & y-5=0

➙y= 4 & y = 5

Put y = 4 ,5 in Equation 1

At y = 4

➙x= 9-y= 9-4=5

x= 5

At y = 5

➙x= 9-5= 4

x= 4

Hence,the numbers are either 5 & 4 or 4 & 5.

Answer 2

Answer:

No real value of x is possible. so question is incorrect

Step-by-step explanation:

Given,

Sum of two numbers = 9

Sum of their reciprocal = 9 / 20

To find: The numbers

Solution:

Let the one number be x.

Then another number = ( 9 - x)

Then the equation formed will be,

i) Sum of the two natural numbers is 9

x + y = 9 …(1)

(ii) Sum of their reciprocals is 9/20

1/x + 1/y = 9/20

(x + y)/xy = 9/20 … (2)

Using (1) in (2)

9/xy = 9/20

xy = 20 …(3)

Using (1) in (3)

x(9 - x) = 20

x^2  -9x + 20 = 0

(x - 5)(x - 4) = 0  

x = 5 or x = 4 …(4)

Using (4) and (1),  

If x = 5, then y = 4.

If x = 4, then y = 5.

The two natural numbers are 4 and 5.