Question

The sum of two numbers is 18. The sum of their reciprocals is ¼. Find the numbers.​

Answer 1

Answer:

Let the first number be x and the second number be 18 - x. Their reciprocals will be = 1/x and 1/(18 - x) respectively. Now, according to the question. So, the two numbers are 6, 12

Answer 2

Answer :-

6 and 12.

Explanation :-

Let,

• First Number = x.

As per Question,

• Second Number = 18 – x.

Now,

Sum of their reciprocals = $\sf{\dfrac{1}{4} }$

According To The Question,

$\dashrightarrow{\sf{ \dfrac{1}{x} + \dfrac{1}{18 - x} = \dfrac{1}{4} }}$

$\dashrightarrow\sf{ \dfrac{18 - x + x}{18x - {x}^{2} } = \dfrac{1}{4} }$

$\dashrightarrow\sf{72 = 18x - {x}^{2} }$

$\dashrightarrow\sf{ {x}^{2} - 18x + 72 = 0}$

$\dashrightarrow\sf{ {x}^{2} - 12x - 6x - 72 = 0}$

$\dashrightarrow\sf{x(x - 12) - 6(x - 12) = 0}$

$\dashrightarrow\sf{(x - 6)(x - 12) = 0}$

There can be only two numbers.

6 and 12.

So, The Numbers are :- 6 and 12.