if sum of the two numbers is 18 the sum of their reciprocals is 1/4 then what are the two numbers
Answers
Answered by
160
The two numbers are 12 and 6. See the attached file for solution. Thanks
Attachments:
Answered by
318
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.
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.
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.
Similar questions