Question

the sum of two natural numbers is 9 And the sum of their reciporals is 1/2. find the numbers​

Answer 1

Answer:

x=6 or x=3

Step-by-step explanation:

sum of two natural numbers 9

X+y=9------(1)

y=9-x-----(2)

sum of their reciprocal 1/2

1/x+1/Y=1/2

X+y/xy=1/2

2(X+y/xy)=1

substitute ( 1) in( 2)

2∗9=1xy

⟹18=x(9 - x)

⟹18=9x - x^2

⟹x^2 −9x+18

⟹x^2 −6x - 3x+18=0

⟹x(x - 6) - 3(x - 6) = 0

⟹(x - 6)(x - 3) = 0

∴x=6orx=3

Answer 2

Given :

• The sum of two natural numbers is 9 and the sum of their reciprocal is 1/2.

To Find :

• The Numbers

Solution :

➟ Let the First Number be x

➟ Let the Second Number be 9 - x

⠀

According to the Question :

⟶⠀1/x + 1/9 - x = 1/2

⟶⠀9 - x + x/x(9 - x) = 1/2

⟶⠀2(9 - x + x) = x(9 - x)

⟶⠀18 - 2x + 2x = 9x - x²

⟶⠀18 = 9x - x²

⟶⠀18 - 9x + x² = 0

⟶⠀18 - 6x - 3x + x² = 0

⟶⠀x(x - 6) - 3(x - 6) = 0

⟶⠀(x - 6) (x - 3) = 0

⟶⠀x = 6 or x = 3

⠀

So, The Two Natural Numbers are 6 and 3

___________________