Question

The sum of two numbers is 15 and the sum of their reciprocal is 3/10. Find the numbers. ​

Answer 1

Step-by-step explanation:

let the two numbers be x and y.

x + y = 15

1/x + 1/y = 3/10

x+y/xy = 3/10

x + y = 15

x = 15-y ----(1)

15-y + y / 15y - y^2 = 3/10

15/15y-y^2 = 3/10

150 = 45y - 3y^2

3y^2 - 45y + 150 = 0

3(y^2 - 15y + 50) = 0

y^2 - 15y + 50 = 0

y^2 - 5y - 10y + 50 = 0

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

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

y = 10 or y = 5

case 1

y = 10

x + 10 = 15

x = 5

case 2

y = 5

x + 5 = 15

x = 10

so the numbers can be 5,10 or 10,5.

Answer 2

→ Let one of the number be = x

→ Other number is = ( 15 - x )

→ Sum of their reciprocals = 3/10

→ 1/x + 1/(15-x) = 3/10

→ (15)/ (15x - x2) = 3/10

→ 150 = 45x - 3x2

→ 3x2 - 45x + 150 = 0

→ x2 - 15x + 50 = 0

→ (x - 10) (x - 5) = 0

→ x = 10 or 5

Therefore, the numbers are 10 and 5

If x = 15

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