Question

The sum of two numbers is 9 and the sum of their reciprocal is 1/2. Find the number.

Please answer quickly, cuz I have exam tomorrow.

Answer 1

Let the two number be X and Y respectively
X+Y is equal to 9
1/x+1/y=1/2
x+y /x*y =1/2
x*y /x+y=2
x*y=18
Solving both equation we get x=3,y=6
Or x=6,y=3

Answer 2

Let one number be x.

The other number is 9 - x.

.

The sum of their reciprocal is 1/2:

$\dfrac{1}{x} + \dfrac{1}{9 - x} = \frac{1}{2}$

Combine into single fraction:

$\dfrac{9 - x + x}{x(9 - x)} = \dfrac{1}{2}$

Combine like terms:

$\dfrac{9}{x(9 - x)} = \dfrac{1}{2}$

Cross multiply:

$x (9 - x) = 18$

Distribute x:

$9x - x^2 = 18$

Keep all to LHS:

$x^2 - 9x + 18 = 0$

Factorise:

$(x - 3)(x - 6) = 0$

Apply zero product property:

$x = 3 \ or \ x = 6$

.

When x = 6

One number = x = 6

The other number = 9 - 6 = 3

.

Answer: The number is 3 and 6.