Question

Divide 27 into two parts such that the sum of their reciprocals is 3/20

Answer 1

Answer:

Step-by-step explanation:

let one of the number be x

therefore, other no. will be 27-x

ATQ,

1/x+1/27-x =3/20

By taking lcm,

27-x+x/x(27-x) =3/20

27*20=3(27x-x^2)

540 =81x-3x^2

3x^2-81x-540

3(x^2-27x-180)

x^2 - 12x - 15x + 180

x(x-12)+ 15(x-12)

(x-12)(x+15)

X= -15 and 12.

reject= -15

first part= 12

other part 15

Answer 2

Let number = x

Another number = 27 - x

According to question;

1/x + 1/(27 - x) = 3/20

(27 - x + x)/(27x - x²) = 3/20

Cross-multiply,

20(27) = 3(27x - x²)

540 = 81M - 3x²

x² - 27x + 180 = 0

x² - 15x - 12x + 180 = 0

x(x - 15) -12(x - 15) = 0

(x - 12) (x - 15) = 0

x = 12, 15