Question

Sum of 2 numbers is 18 the sum of thier reciprocals is 1/4 find the numbers

Answer 1

Answer:

the two numbers are 6 and 12.

Step-by-step explanation:

Solution:-

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.

1/x + 1/(18 - x) = 1/4

Taking L. C. M. of x and 18 - x and solving it, we get

(18 - x + x)/(18 - x)x = 1/4

(18*4) = (18 - x)x

72 = 18x - x²

x² - 18x + 72 = 0

x² - 12x - 6x - 72 = 0

x(x - 12) - 6(x - 12) = 0

(x - 6) (x - 12) = 0

x = 6 and x = 12

So, the two numbers are 6 and 12.