Question

The sum of two natural numbers is 9 and sum of their re iprocals is 9/20 find the numbers

Answer 1

THE TWO NUMBERS ARE 4 AND 5

SOLUTION:-

Let the numbers be x and y

GIVEN:-

• Sum of the two natural numbers is 9

x + y = 9 …(1)

• 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.

Answer 2

Answer:

4,5

Step-by-step explanation:

Let x and y be two natural numbers.

x + y = 9 --(1)

1/x + 1/y = 9/20

y + x/xy = 9/20

9/xy = 9/20

xy = 20

x = 20/y

Substituting in equation (1)

20/y + y = 9

20 + y²/y = 9

20 + y² - 9y = 0

(y - 5) & (y - 4) are roots of the equation.

y can be 5 or 4

x can be 4 or 5

Hope it helps.....