the sum of the reciprocal of two number is 1/2 twice the reciprocal of the sixth less than five times the reciprocal of the 2nd. what are the original #?
1/x + 1/y = 1/2
I cannot parse the second sentence.
The reciprocal of the sixth less than five times
The reciprocal of the 2nd.what are the original number
you should have completed the solution ;A;
To solve this problem, let's assign variables to the two numbers in question. Let's call the first number "x" and the second number "y."
According to the problem, the sum of the reciprocals of the two numbers is equal to twice the reciprocal of the sixth less than five times the reciprocal of the second. Mathematically, this can be expressed as:
1/x + 1/y = (2 * (1/6 - 5/y))
To simplify this equation, we can eliminate the denominators by multiplying each term by their respective denominators:
(y + x) * xy = 2 * (xy * (1/6) - 5 * (xy/y))
Simplifying further, we get:
xy(y + x) = xy/3 - 10x
Expanding the equation, we have:
xy^2 + x^2y = xy/3 - 10x
Now, let's rearrange the equation to bring all the terms to one side:
xy^2 + x^2y - xy/3 + 10x = 0
Now, we have a quadratic equation in terms of "y." We can solve this equation to find the possible values of "y."