Question

Divide 27 into two parts such that sum of their reciprocal is 3 by 22

Answer 1

Let a part is x
Let part b is y
X+y=27
X=27-y
1/y + 1/27-y = 3/22
(27-y + y)/27y- y^2 = 3/22
27 / 27y- y^2 = 3/22
594 = 81y - 3y^2
594 - 81y + 3y^2= 0
y^2-27y+198=0
Do it yourself

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