Question

the sum of two numbers is 18 . the sum of their reciprocal is 1/4 . represent the given situation in the form of a quadratic equation.


no spaming​

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation:

let the two numbers be 'x' and 'y'

according to the question-

x+y = 18  -----------(eq 1 )

1/x+1/y= 1/4  -------------(eq 2)

from equation 1 we can find the value of 'y' as y = 18-x

=> substituting the value of in equation 2

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

72=18x-x²

x²-18x+72  {required quadratic equation in x}

(x-12)(x-6)  [factors of the above quadratic equation]