Question

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

Answer 1

sol:-

let the first no. be x and second be y.

According to the First and second Condition:-

x + y = 15 .....1

1/x + 1/y = 3 ....2

now,

1/x + 1/y = 3

(y + x)/xy = 3

(x + y) = 3xy

15 = 3xy ...from1

xy = 5

multiplying the both the side by 2

•°• 2xy = 10 ......3

now,

=> x+ y= 15

squaring both the side :-

•°• (x + y)² = 15²

x² + 2xy + y² = 225

(x² + y²) = 225 - 2xy

(x² + y²) = 225 - 10 ...from3

x² + y² = 215 ......4

now,

(x - y)² = x² - 2xy + y²

(x - y)² = (x² + y²) - 2xy

(x - y)² = 215 - 10

(x - y)² = 205

x - y = √(205)

x - y = 14.31 .......5

now, x + y = 15 and x - y = 14.31

Adding equation 1 and 5

x + y = 15

+ x - y = 14.31

2x = 29.31

x = 14.65

substituting x = 14.65 in equation 2

14.65 + y = 15

y = 15 - 14.65

y = 0.13

The numbers are 14.65 and 0.13

note: √(205) = 14.3178210633 approx 14.31