Question

The sum of two Numbers is 15. If the sum of their reciprocals is 3/10,. find the numbers

Answer 1

Step-by-step explanation:

let the 2 nos be X and y

X + y = 15

X = 15-y

and

1/X + 1/y = 3/10

10x + 10y = 3xy

put X = 15-y in above equation

10(15-y) +10y = 3(15-y)y

150 +0 = 3(15y-y²)

15y - y² = 50

y²-15y+50=0

y² -10y-5y +50 =0

y(y - 10) -5(y-10) =0

(y-5)(y-10) = 0

y = 5 or y = 10

so following nos are

5 and 10

Answer 2

Given :

• The sum of two numbers = 15.
• Sum of their reciprocals = 3/10

To Find :

• The Numbers

Solution :

Let the numbers be α , β

Sum of the roots = α + β = 15 ---------> (1)

1/α + 1/β = 3/10 ---------> (2)

β + α / αβ = 3/10

10 ( α + β ) = 3αβ ---------> (3)

3αβ = 10 × 15

= 150

Product of the roots = αβ = 50 ---------> (4)

→ From (1) and (4), we have

x² - 15x + 50 = 0

( x - 10 ) ( x - 5 ) = 0

→ x = 10 , 5

•°• Hence, The Numbers are 10 , 5