Question

If the sum of 2 numbers is 9 and the sum of their reciprocals is 1/2.Find the numbers

Answer 1

Let the numbers be x and y.




x + y = 2 … (1)

1/x + 1/y = 9/4 … (2).

4x + 4y = 9xy … (3).

4x + 4y = 8 … (4).



From (3) and (4), we get

9xy = 8

9x(2-x) = 8

-9x^2 + 18x -8 = 0, or

9x^2 - 18x +8 = 0, or

9x^2 - 12x -6x +8 = 0,or

3x(3x-4) -2(3x-4) = 0

(3x-2)(3x-4) = 0





Therefore x = 3/2 or 4/3 and the corresponding values of



y are 2–3/2 = 1/2 or 2–4/3 = 2/3.

The two pairs of fractions are: 3/2 and 1/2 or 4/3 and 2/3.

Answer 2

x + y =9 => x= 9 - y
1/x +1/y =1/2
=> 1/(9-y) + 1/y = 1/2
=>(y+9-y)/y(9-y) =1/2
=>9/(9y -y^2)=1/2
=>18 =9y- y^2
=>y^2 -9y + 18 =0

Solve the equation
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